Alright, I hope this helps Hexagram 13 (and anybody who might decide to yank linoleum up).
After looking into, and trying, a few different methods, I can offer this piece of advice......
....Go the chemical route.
The only thing that worked that wasn't a total pain in the ass was a product called EZ-UP.
Now this stuff has some serious vapors. So don't do this in the winter, as you will have to open up all the windows to ventilate.
But if you rip the actual linoleum up (the top plastic part anyway), you'll be left with the adhesive. Dilute this EZ-UP (bought at Lowes) stuff, spread it on your floor, let it sit for an hour, and scrape it up (with a big floor scraper). Works like a champ. And saves alot of wear and tear on the body. Seriously, this stuff comes right the hell up.
I can't believe I even rented that damn machine yesterday. It didn't work worth a crap. And wore my ass out.
Anyway, just a piece of advice in case you come across the same situation.