(1,0) / (3,0) / (-1,-1) / (-2,1) / (-1,0)
or
-2,0/3,0/-1,-1/-2,1/
or
1,0/0,3/-1,-1/1,-2/
or
0,-1/-3,0/1,1/2,-1/
work best for adj/adj swap.
Depending on the EP case you can use these to swap adjacent edges on the top and bottom layer.
parity is when two edges are swapped (adjacent or opposite)
If you have a z perm (two adj swaps on one layer) or adj/adj (two edges swapped on top layer and two edges swapped on bottom layer), you do not have parity.
There is no double parity on sq1 like there can be on 4x4
I think that there are many aspects that can/will be explored in the future. Like you said, some will seem useless and random. But I can see several recent innovations be perfected or tested still.
Ridges/concavity
weighted corners/pieces (or lack of weight)
size (smaller and larger cubes)...