MCELL (3x3x3 method)
Improvements for 2H: combine steps 3-5 as 3) rotate after 2x2x2 is finished
4) WV the corners
5) L5E(ish)- orient the remaining edges and solve the D-face piece
6) PLL
OR
(more efficient but more algs that aren't as nice)
3) TCLL
4) L5E
(both straight)
Movecount (in STM, for SQTM add ~3 moves) <45- (easily)
<40-(better at block building still x2,y CN)

5? (definately possible to average this in my opinion)
Breakdown in STM (mine): roux block:8
2x2x2: 10
pair+insert: <6- sometimes I did the pair during the F2L-2 (missing edge and ce pair) where it averaged about 4-5
CMLL:10
L5E (L5EOP which is slightly less efficient): <10
Total: <44 (I didn't even use TCLL when I was doing the solves and it is speed rather than movecount optimised)
Pros: ergonomic (especially compared to other methods that have a similarly low movecount (except maybe Snyder2))
Low movecount
Good lookahead
no abstract concepts like Eoline/edge
Cons: lots of algs for CLS (but the way I do it is still quite efficient with CMLL)
rotation could be disorientating but you could just do Rw&R moves rather than Uw &U which would make this a rotationless method
Could be quite a fast method in my opinion unless you don't do block building.
Further movecount reducing stuff (but not necessarily better for speed):
1) form 3 2x2x1 blocks with one colour face in common (like heise but without the centre-edge-centre 1x2x2 heise block) (well, I can always do it in <16 STM but someone who is really good at heise blocks can probably do it in <12 STM, maybe average ~10 STM)
2) move to form an F2L-2 (+orient remaining edges) (~5 STM)
3) TCLL (preserving orientation) (~9 HTM)
4) L5E (just permuting) (6.7 STM)
Total: <~30? (STM as well as about the same in SQTM, perhaps even lower in ATM or AQTM) (apparently about the same movecount as Snyder3 but is actually published and the algs are actually known)
Only issue is that the 2 slots (for the edge and the corner) are not always adjacent so it's probably the problem when it comes to speedsolving.
Also, this uses a new(?) LL/double LS variant: L5E, L5C (or TCLL)
Pros
Very low movecount
3-look method
1LLL (if we use 5 cycles for corners)
Still about the same number of algs as CFOP and far less than (for example) ZBLL
Few rotations (potentially none if done correctly)
Can be transfered directly to 2x2x2 where it averages <14 moves (not even CN) and is a 2-look method (although you could lookahead like in actual TCLL)
Cons:
Very heavy reliance on inspection
Orienting edges while doing the blocks could be difficult for a beginner
Still a fair few algs to learn (~84 for TCLL, do the L5E intuitively
Summary: I don't really know what to say here: this could be fast but it would require very good block building (but no worse than that of roux or petrus), the LS/LS style of LL can easily be combined with many other methods as well (notably ZZ where it could give a 1LLL)
Variations with easier F2L-2
CFOP: partial cross (~4 moves), 3 pairs- you could use a ZZ style approach (12 moves), orient all edges (6 moves), TCLL (9 moves), L5E (7 moves)- ~38 moves
ZZ: Eo (6 optimal, 7 realistic) FB+1 pair+1 edges (13 moves), TCLL (9 moves), L5E (7 moves)- ~35 moves
Petrus: 2x2x3 (10 moves), pair (3 moves), orient edges+place the last 2nd layer edge (7 moves), TCLL (9 moves), L5E (7 moves): 35 moves
Average: 35.666... Moves
For future reference I'll probably call this method MCELL (Missing Corner Edge Last Layer solution)
What does everyone else think?