The next step is now to get it to work
without getting hit. Currently, the most plausible approach is to use the inside-of-enemy technique. You can mustache jump on the first koopa, then after landing on the platform, you can stay inside of it. When the second koopa is approaching, proceed as normal. Problem is that the jump you gain from landing on enemies are random (at least I think they are) in height. You need to be facing left and bump into the wall to use the no-scrolling technique.
So sometimes when mustache jumping, you would bump into the corner, but not make it on the platform. Sometimes you would land on the platform without touching the wall. And sometimes you can make it on the ground while having bumped into the corner. But I was only able to land on the platform with next to zero acceleration. So this made the no-scrolling trick kind of inefficient. I haven't figured out yet what determines the randomness behind the random jump heights.
http://dehacked.2y.net/microstorage.php/info/502710249/4-3_problem-not-hurt.fcm
This is the approach.
Note that I posted the 4-3 solution right after I found it. I didn't have another try at it, so it might be possible to get it to work with less space in the gap on the left. (Although, right now as I'm typing this here, I think I had actually checked this. No idea...) Currently, I'm rather demotivated to have more tries at that 4-3 level again.
edit: Oh, and thanks for the cheers concerning my 4-3 solution earlier! :P