To be honest, from my experience at least, this is normally caused by something like an array out of bounds error that doesn't cause the program to completely crash. Instead, the program will exit the function that caused the error and continue processing the rest of the code. Chances are, there is an "updatePlayer" function or something like that that calculates physics, processes button pushes, etc., but ends up getting completely skipped in all the game loop updates. For whatever reason, the 3rd extra accessory slot seems to be causing those types of symptoms.Yea.. I hit the wall with the same thing... Well, good luck to you.
I think Eldrazi found a way to work around it, but nobody has seen him for some time.
EDIT: From Eldrazi's thread, this seems to confirm what I suspect: https://forums.terraria.org/index.php?attachments/crash_error-jpg.98877/
Why the game crashes at 3 extra slots and still allows the 2nd extra one is one great mystery. I suspect only the Terraria devs themselves may be able to find out.
EDIT2: OK here's my best guess. The array that holds the extra accessory slots is hard coded to store 7 records. By setting extraAccessorySlots to 3 or higher, we are forcing that array to attempt to store more values that it is able to hold, and thus the crash. Unless we can actually access that array somehow and modify its size, there is likely no possible way to do anything about this.
This is, of course, assuming that this is the problem. I am pretty sure that it is though.
EDIT3: After thinking about it a bit more *and* realizing that the cheat sheet mod is able to add multiple accessory slots beyond the 3rd, I suspect that the bug has to do with the dye and/or vanity slot, and not in fact the accessory slot itself.