Well, apparently I was wrong in my calculations; the best I can come up with without using L+R is 1,360,000 even. (2 frames faster and I could have gotten 1,360,550; 6 more, and I would have gotten 1,365,000)
Annoyingly, if you get a coin in the bonus area, then the Hammer Bros. will be placed differently and you can't kill them at full speed. I guess you could probably manipulate the frame you get there at; hopefully it wouldn't take another 18 frames to get a favorable arrangement. Also, getting the 10,000 hit from the last Koopa before the stairs isn't possible without either missing the other Koopa at the end or taking too many extra frames for it to be worth it; I might have gone with hitting it to the left to make the shells collide, but when I tried that,
this happened.
I'll play around with L+R for another run, but I think 1,360,000 might be maxed for no L+R (at most, 1,360,200). With it, 1,365,000 should easily be possible, maybe even 1,370,000+.
EDIT: Going to try to finish my L+R-less version first. I did manage to save a couple frames on the stair section and get 1,360,550, but I need five more frames to get it any higher.