Using solvents to remove flooring is never a really good idea, most have a low flashpoint, which puts you at risk of fire or explosion. Then residue left over from the solvents can cause problems with adhesives and the new floor covering.
The best thing I have found for removal has been a long handle heavy duty scraper with replaceable blades. The scrapers are heavy metal and will dig right under the floor covering. The commercial stripping machines are good, but will leave you needing to finish some areas by hand anyway.
This one, the model 375 has an 8" blade and a 59" handle.
No easy solution, sweat and a heavy scraper is the best. A hot air gun may help, but some adhesives will not respond to heat at all. The old flooring will just delaminate and you will have backing still stuck to the floor.
Whatever you do, you may need a coat of floor leveler when you're done. Just a skim coat. It will dry quickly, so don't mix much at a time. After it sets, you can sand it a bit and get a smooth finish.