If LU/RU are different: align M-edges and do the obvious.
If LU/RU are the same: align L/R-edges and do the obvious.
Writing it this way is much less precise, but it emphasizes how easy (and helpfull) it is.
(especially helpfull, if you missed the lookup step in Athefre's method, because of...

Do you like/dislike any of the following subsets:
- Edges solved
- Edges phased
- Edges 3-cycle
I always feel like the 3-cycle set has the best algs, but since it is the biggest set and I only know very few(the best) algs, this kind of feelings might be completly wrong.

Last 2 Layers EP5
Hijacking your 1st Step:
1. LS-Corner + EO
2. COLL
3. Last 5 Edges
Last 5 Edges is mostly U-, Z-, H-Perm variations and just 6 new algs (with pretty good recognition)
The LS-Corner+EO Step can also be shortened, bcause ther is no real need to orient the F2L edge - instead...

Something I use for LS-Corner already placed, but LS-Edge somwhere on U-layer.
1) CLL + 2) Solve F2L-Edge and one LL-Edge + 3) Last 3 Edges
The algs for 2) and 3) are almost the same, and edge 3-cycles (~75%) are pretty fast to execute
If CLL solves an edge, you can replace 2) and 3) with...

Your times are much better than mine, but I used to get rid of the step like this.
1. Solve a 3x2x1 like in Roux (six white stickers)
2. Solve ANY 2 of the belt-edges to form a pseudo 3x2x2
3. EO
4. mixed Layer F2L
...
Mixed Layer F2L is much better and easier than it sounds. eg. instead of...

I checked all cases manually to correspopnd to my recognition system. There can also not be an additional case so the recognition system is complete.
I did only a few sample solves and found that after knowing the FUL-FUR relation just one sticker on URB is often enough to tell the FUR-BUR...

Case Reduction 24 -> 6
There are 24 cases how corners move, but only 6 names to it ... then there should be a recognition system that only has 6 cases, right? (formal context analysis is the math terminus I think)
Two adjacent corners can have exakty one of this three relations:
1. Pair - The...

Even with Corners permutated and Edges phased there are still 28 cases left [ (7 corner patterns) times (solved + H + Z + Z) ] - maybe a learning step to full 2GLL
But how to do the "permute corners while finishing left block" step. Even with "infinite" time I don't find a logic how to fix cp.

I discovered the following 2-Step zz-blah Last-Layer simplyfication:
Edge-Permutation and Corner-Orientation can always be solved by doing a two SUNE combo. One of the 4 CPLLs (A,A,H,E) to solve the cube finaly.
How to find the SUNE combo?
a) For corners: the first sune must set up a SUNE...

Even 800% will not make me a millionair in todays lottery, I was thinking more of the small things that really happen alot, like this F2L-Slot pieces that just pop into my view, just the moment I need them, but you will argue thats just my lack of blockbuilding skill - so be it.
Finally an...

As much as I like something new in this buisness, I really doubt there is any method a human can execute faster than CFOP - reasons:
- Cross is easy to learn + good cubers say they already find the first slot solution while doing the cross.
- while cube rotation seems bad it also means solving...

On Petrus Website it is stated, that not breaking parts of the cube, that are already build, is one idea wich inspired Petrus to make up the methode as it is.
-But for sure there is no proof that this principle yields a better movecount in every case.
-the EO step itself contradicts this...

If I add a Z-Perm to the Setup M' U2 M' U2 M2 U' M2 M2 U M2 F2 M2 F2 U' M2 - I still have some sort of bar to the left, but M2 U M2... if no good anymore.
Next I tried M' U2 M' U2 M2 U' M2 E2 M' E2 M - A real bar to the left again, but M2 U M2... is still no good.
I feel like you...

Wow, this is the first complete list of Fish algs I've ever seen. (P.S case 1-7 is easier solved by a plain Niklas RU'L'UR'U'LU )
I also considered antiphasing:because if you antiphase and you have a corner edge pair the fish step can always be done as a Sune or as a J-Perm
(In pased case...

If I see an easy 3x2x1 at the beginning I alwas start my petrus solves with this block, though I don't care about edges orientation at all, while placing the D edges.
This is a collection of my thoughts, I had about this idea. (I found it to difficult to use in speedsolves, and focused on...

My prefered alg for CP would be D'RUR'D
Even if there are only 6 cases, is there a beginner rule how to solve cp iterativly(like the way you learn EO for Petrus )

I once had the idea to learn one edge-preserving COLL and one "phase-correcting" COLL (that's half of ZZ-b).
- This makes for 50% last step skip.
- Last step (if no skip) is always an H, wich is AUF free.
- Recognition is much simpler: you just need COLL recog because you will get to know the...

Most of th algs in Your list are not RU. In fact if most of them where RU, there might be an easy way to narrow down the options for Step 2 (seperation and permutation).