I decided I should test what I just suggested so I...
Downloaded the 64bit static release of ffmpeg for Windows and unzipped it to my desktop allowing it to reside in the folder it created.
I then downloaded the latest nightly build of OpenToonz...
Uninstalled my previous version of OpenToonz... (just so I know I'm starting with a pretty clean slate)
Installed the latest nightly build of OpenToonz...
Went into Preferences (on the Import/Export tab) and pointed Opentoonz to the ffmpeg folder on my desktop (specifically I pointed it to the bin folder. That's where the required convert.exe file is)
I then tested a gif render and it worked... the first time.
Then... it didn't want to work again.
Doh.
So... I renamed the ffmpeg folder on my desktop from its very long name to just 'ffmpeg'.
This is just in case the program has issues with really long paths and file names (I don't claim this is really an issue... just insurance against running into the issue if it does ever exist)
And... now things appear to be working as intended.
Yay! Hope the same works for you as well. :)