I ended up making one of the Mega Drive/Genesis cartridge adapters. I won't post a pic here because my soldering is atrocious.
I did about a dozen or so games and they all dumped fine with the exception of two. But I think the bad dumps for those two are due to the filth factor of their connectors. When I get some time later I will clean them and re-dump them.
I was pretty excited to be able to dump my Genesis games! Thanks again Sanni for the hard work!