Thanks to Michael Fried's idea, we now have a SMB2j submission that completes the game 22 frames faster than the previous version.
It would actually be ~30 frames faster if the game didn't have the Censorship Of Great Deeds principle, which basically means that the completion times of all scenes are rounded up to the next 21 frame granularity (same as in SMB1).
It also has a slightly lower final score and less coins than the previous version (how's that an improvement?). It stomps some enemies that it didn't stomp the previous time.
Unfortunately I still wasn't able to Force the piranha plants out from my way, so I had to wait in the usual spots.
The completion time is 08:21.43
The completion time of the previous version was 08:21.79
Hey, at least it rounds towards 21 instead of 22 now :)

I created this movie by rerecording the previous version -- starting from the second part of level 1-2 (without discarding the rest of the movie) and then replaying miscellaneous scenes from all levels, beginning with the ones that desynced because of changed monster locations (mostly bullets).
About 30% of this movie is identical to the previous version.
I think I'm starting to be somewhat experienced in editing of the movie files. Note that this does not conflict with the spirit of this site - the games are not modified. I wouldn't mind even if the entire movie (still talking about the keypad input) is computer generated. Actually, that could be exciting to see :)

Submission file updated: Now includes a little more interesting playing in the 1-2 level. This increased the rerecord count by 193 (reflected by the submission header).
An FCEU version is available at: https://files.tasvideos.org/common/SubmissionFiles/459S/bisqwit-smb2j-v6-converted.zip