The answer is that top Roux solvers ALREADY perform a degree of edge orientation during CMLL. They inspect edge orientation and choose one of two CMLL algorithms for that case, such that, the edge flipping of the CMLL algorithm prevents L6E from having the 6-flip case which is the worst case. Based on their real world application, it seems that is the maximum amount of edge orientation that is worthwhile, during CMLL. Any more is probably not worth the trouble.
Waterman in the 90's experimented with solving edges while executing the corner algorithm, by doing wide slice moves on the CLL algorithm you can modify the edge effects, but, generally the recognition is very poor as there are so many edges to examine.