Someone needs to invent Alaskan Kociemba. You already have the hard part(The name), so it shouldn't be too hard. Anyone who invents it will get early access to my website.
Given my limited geography knowledge, I believe Hawaii is the tropical end and Alaska is a arctic end of the tropical-temperate-Arctic spectrum.
Plus, I believe Kociemba is a family name.
So Alaskan Kociemba should belong to the same family as Hawaiian Kociemba, but should feel arctic rather than tropical somehow. Hmm..
How about the following:

Step 1: Orient all F2L edges (8 edges) while solving the edges in DB, DL and BL (while ensuring that the DBL corner is some top layer corner)
Step 2: Solve the FL square and Right block like in ZZ, to get F2L minus one corner.
Step 3: Use AK-OLL to orient all edges and corners (I guess ~170 algs, 57 of which are OLLs)
Step 4: Use AK-PLL to permute everything (93 algs, basically TTLL + PLLs)

Step 1 is the same amount of work as HK (EO of 8 edges, placing 3 of them).
Step 2 is the same amount of work as HK, solving 2 squares and 1 pair instead of 4 pairs, and also has fewer blindspots.
Step 3 has similar number of algs as HK-OLL, and similar recognition.
Step 4 is already completely developed, and has similar number of algs as HK-PLL with better recognition.

You could have better speed with the variant where you also solve the DF edge in step 1; which leave you with only right block and FL slot for second step, and thus requiring no F2 moves plus better look ahead. People solve EO crosses in inspection, this should be doable given we aren’t orienting top layer edges.

Its the same family, just look at how similar these methods are. Thus, Kociemba.
Hawaii is on one side of the country, its like an "edge", that's what remains after F2L-1piece; Alaksa is at a "corner" of the country, that's what remains after F2L-1piece.

Alaskan Kociemba People!
 
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Given my limited geography knowledge, I believe Hawaii is the tropical end and Alaska is a arctic end of the tropical-temperate-Arctic spectrum.
Plus, I believe Kociemba is a family name.
So Alaskan Kociemba should belong to the same family as Hawaiian Kociemba, but should feel arctic rather than tropical somehow. Hmm..
How about the following:

Step 1: Orient all F2L edges (8 edges) while solving the edges in DB, DL and BL (while ensuring that the DBL corner is some top layer corner)
Step 2: Solve the FL square and Right block like in ZZ, to get F2L minus one corner.
Step 3: Use AK-OLL to orient all edges and corners (I guess ~170 algs, 57 of which are OLLs)
Step 4: Use AK-PLL to permute everything (93 algs, basically TTLL + PLLs)

Step 1 is the same amount of work as HK (EO of 8 edges, placing 3 of them).
Step 2 is the same amount of work as HK, solving 2 squares and 1 pair instead of 4 pairs, and also has fewer blindspots.
Step 3 has similar number of algs as HK-OLL, and similar recognition.
Step 4 is already completely developed, and has similar number of algs as HK-PLL with better recognition.

You could have better speed with the variant where you also solve the DF edge in step 1; which leave you with only right block and FL slot for second step, and thus requiring no F2 moves plus better look ahead. People solve EO crosses in inspection, this should be doable given we aren’t orienting top layer edges.

Its the same family, just look at how similar these methods are. Thus, Kociemba.
Hawaii is on one side of the country, its like an "edge", that's what remains after F2L-1piece; Alaksa is at a "corner" of the country, that's what remains after F2L-1piece.

Alaskan Kociemba People!
If you Start with ZZ EO than solve The Dl DB DF edges aswell as the L And BL edges Do L and BL edges than solve the other edges with the Right side you can use something like SSC method keyhole to solve the 2x2x3 than with edges already oriented finish the other 2 pairs.(while holding the unsolved cross piece on right)
Than just rotate for HKOLL/PLL
this version would be bassically just a zz variant though lol...
You could also use CMLL+ HKPLL instead of HKoll/pll
The reason to do this with the rotation is for superior fingertricks.
A proposal for Alaskan-Kociemba.
Also the finger tricks are good which makes it maybe better for OH
as a break from cfop im gonna learn the l5e variant of kociemba (=
 
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A LEOR variant that I think may be a little more efficient:

LB
EO(not stripe)
RB
M-Slice
ZBLL

Basically you go straight from EO to RB and solve DF+DB later. For me, DF+DB takes a bunch of moves after doing EO, but with RB already solved it usually only takes 5 or so moves. RB is hindered much(if at all) because using M2 allows for pairing in the M-slice easily. Example solve:

Scramble: D' L' D2 L' U2 L' B2 D2 R2 B2 F2 R D2 F' R2 D' B L' B' U2

F' E' L' F D2 F2 S M S' // LB

x2 S' U S R' U F R F' // EO

r2 U M2 U2 R' U R U' M2 U2 R U R' // RB

U' M U2 l // Stripe

y2 U R' U R2 F2 R' U2 R' U2 R2 F2 R2 U2 // ZBLL

I'm bad at blockbuilding, so LB and RB could definitely be more efficient


EDIT: Did a couple example solves on other threads, am averaging mid 40s, I imagine you could get sub-50 during a speedsolve with some practice and advanced techniques
 
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Not sure if this has been thought of already, let me know if it sounds familiar. 5x5 Method:
  1. Solve one center
  2. Solve three other 2x2x3s of center pieces around the initial center with the block oriented toward the first center on D, F, and B. If this doesn't make sense I can post pictures.
  3. Use the free Rw slice on the right to make the LF and LB F2L edges and pair them with the corner to make the F2L pairs and insert.
  4. Solve the bottom center, rotations are ok.
  5. Solve the DF left wing and midge, and the DB left wing and midge without disturbing centers.
  6. Finish F and B centers
  7. Solve remaining DF and DB wing by oreinting it so the cross color is on top and the wing is in the UB position. Then do Rw U2 Rw' U2 Rw U2 Rw' U2 Rw U2 Rw' to solve it repeat in the back
  8. Rotate to finish centers
  9. End with Yau5 sort of reduction to 3x3 stage.
 
Not sure if this has been thought of already, let me know if it sounds familiar. 5x5 Method:
  1. Solve one center
  2. Solve three other 2x2x3s of center pieces around the initial center with the block oriented toward the first center on D, F, and B. If this doesn't make sense I can post pictures.
  3. Use the free Rw slice on the right to make the LF and LB F2L edges and pair them with the corner to make the F2L pairs and insert.
  4. Solve the bottom center, rotations are ok.
  5. Solve the DF left wing and midge, and the DB left wing and midge without disturbing centers.
  6. Finish F and B centers
  7. Solve remaining DF and DB wing by oreinting it so the cross color is on top and the wing is in the UB position. Then do Rw U2 Rw' U2 Rw U2 Rw' U2 Rw U2 Rw' to solve it repeat in the back
  8. Rotate to finish centers
  9. End with Yau5 sort of reduction to 3x3 stage.
Do you think this could be effiecient/fast?
 
Do you think this could be effiecient/fast?
The limiting factor feels like the 3rd step. I haven't done movecount tests but it feels like less than redux
The idea came from doing scrambles using R Rw U and Uw and seeing if I could solve with just those moves. I did and thought, "Maybe if I reduce to this it could be cool."
 
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Redux is more efficient than yau/hoya, if you can get good tps this is huge. Also please post the pictures.
What is the movecount for redux or hoya?
 
New(?) method for LS+OLL: First, solve LS corner+EO. Then, solve LS edge+CO. This is similar to MGLS, but I believe it has less algs, though I don't know about effeciency. The first step has around 18-36 algs, including mirrors, and the second step should just have 14, 7 excluding OCLL. Has this been proposed before, and if so, are there algs anywhere for it?
 
New(?) method for LS+OLL: First, solve LS corner+EO. Then, solve LS edge+CO. This is similar to MGLS, but I believe it has less algs, though I don't know about effeciency. The first step has around 18-36 algs, including mirrors, and the second step should just have 14, 7 excluding OCLL. Has this been proposed before, and if so, are there algs anywhere for it?

As you said, this is similar to MGLS. It's been proposed before, but no algs have been genned because MGLS is better and LS->OLL is better than MGLS
 
As you said, this is similar to MGLS. It's been proposed before, but no algs have been genned because MGLS is better and LS->OLL is better than MGLS
Why is it worse? It has less algs then most other LS+OLL methods, and recognition is pretty good. Does it have bad movecount?
 
New(?) method for LS+OLL: First, solve LS corner+EO. Then, solve LS edge+CO. This is similar to MGLS, but I believe it has less algs, though I don't know about effeciency. The first step has around 18-36 algs, including mirrors, and the second step should just have 14, 7 excluding OCLL. Has this been proposed before, and if so, are there algs anywhere for it?
This has already been proposed, and is called JJLS:

Still cool you came up with it though :)
 
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