To remove old vinyl tiles you need the patience of a saint and
Herculean strength. It is, I believe, one of the worst jobs on the
planet! A good floor scraper is a must, but even these do take a lot of
muscle. A hot air gun, applied gently to the adhesive, will loosen it
and allow it to be scraped up as well.

I have a VERY good friend whose dad is in the floor business. He let
me borrow a tool. It had a razor sharp blade, about 10 inches wide and
a 4 -5 foot handle. It was HARD work, but it stripped off the stuff.
I wouldn't want to do a huge floor, but it worked for me. Certainly
took off the big chunks.

I've heard of the self leveling goop, but I didn't want the mess. I'd
rather put in the elbow grease. Heat gun and scraper also work, but
very slow.

The new floor looks great!! I put sheet vinyl over it.

You might visit a rental store and see if they rent the scraper tool.
It was not a power tool, so I doubt it would be too expensive to rent.
375s on this page:
http://www.tiletool.net/Floor_Scrapers.asp

Not that expensive...maybe buy one and let your neighbor borrow it?
But don't offer to help!!!!!!!!

Just a suggestion....