This run is somewhat underappreciated (for one, I've yet to see a comment from adelikat), but it does raise some doubts whether it can't be pushed further.
If stage 6 is indeed slower it may be because player 2 lagged behind too much, making the screen scroll longer (in which case it would probably make sense to suicide p2 at some of the vertical jumping sections). Then again, there might have been another reason.
Can the jumping height glitch normally used in stage 2 be used elsewhere?
Also, player 2 needs more attention.
This run perfectly encapsulates stylish and entertaining interaction between two players. There might be less opportunities for that in Contra, but I think more good things could be done.
That being said, I vote yes. Improving upon one of the better and more researched runs by adelikat is no easy feat, especially for the first submission.