Hey I figured out how to get past this.
I had the exact same problem and tried everything for like 3 hours...
searched and searched..didn't look like anyone ever got it solved..
So I gave up searching and just fiddled with it..and BAM!
This is bumping an old topic but I will post anyway as it is useful information regarding the 1 of the jillions of Paper Mario problems out there.
Anyways-first you need to turn on your Advanced Settings.
Open up Project 64 and go on the top, hit "options", scroll down to "settings...", then hit the "options" tab in the window that pops up, and uncheck the box that says "Hide Advanced Settings" and hit OK.
Now open up Paper Mario, and go to options-->settings again.
And now hit the tab named "Rom Settings"
Then next to where it says Self-modifying code method: change it to "Check Memory Advance" and hit OK.
And it fixed it! I have no clue how but I don't care. There was a similiar solution to the twink and peach cutscene, so I figured I'd mess with that..
and you might want to set the self-modifying code back to what it was on when you get to lavalava island--just in case.
EDIT FEB.29: I was fixing this problem on my brothers computer and it wasn't working, I figured out I had to completely close the PJ64 and bring it back up for the adjusted settings to take effect.