An update on the situation. The movie syncs fine when the system date is May 20 or before. The movie desyncs when the system date is May 21 or the week of May 21. These dates are not exclusive, and the case may be different for other users.
I tested as follows:
May 19, no .sav: Works fine.
May 19, .sav: Desyncs at the Totodile naming screen.
May 21, no .sav: Desyncs when Mom says "Sunday, is it?" (actually, long before)
May 21, .sav: Desyncs after entering the grass, encountering a Sentret.
The date in no way hinders my progress, as I make the movie off savestates.
My progress so far is Bugsy's gym defeated. I'll edit this post when I get the run up.
Edit:
Restarted to fix the mistake primorial#soup pointed out, and here's the run up to Bugsy's gym defeated (with savestates):
http://www.savefile.com/files/5101207
I rerolled, and got a FCFF L3 Geodude. The F speed and special DV's don't hide the fact that the respective stats are bad.
Geodude's lack of speed had me worried for a while, but I hope moves like Rock Throw, Magnitude, and Rollout can make up the difference later on. A Totodile run would be maybe 2-3 minutes faster at this point.
I didn't catch Pidgey yet.