W.W.
L.,
I would hire a company to come in and do a move-in clean that would include the appliances. I know it sounds like a cop-out - it's not. You have a lot on your plate and if the house is empty? It should NOT cost much to do. But will save you a LOT of time...
I believe this is the company that my nephew and his wife used
http://www.greenvalleymaids.com/
and this is who my sister used when a friend of hers died and it was a huge mess....
http://henderson.thecleaningauthority.com/
If you don't want to do that? I would use Easy-Off - spray it on really well, leave it for an hour and move on to something else.
Good luck!!