I've been playing Escape from Monkey Island without ResidualVM, and ran into a bug. I then downloaded ResidualVM and want to continue with my save. Is there a way to convert the file (*.gsv) to the correct format of ResidualVM so I don't have to restart the game?

No, there's no such way, as we don't currently support the savegames of the original game (and are probably unlikely to do so for the foreseeable future). However, there are cheats that enable you to jump to a particular spot in the game (not all of those are fully functional however).

See jump points here:
http://wiki.residualvm.org/index.php/Es ... Debug_Mode

Note the comment about first jumping to the correct act, as the jump points are somewhat more unstable than their Grim Fandango counterparts.

Also beware that you have to enable developer mode by editing your residualvm.ini file (or ResidualVM Preferences / .residualvmrc on OS X / Linux) and adding "game_devel_mode=true" to your EFMI-target.