Dana, Now you know why flooring contractors get the big bucks. Go buy a floor scraper for about 30 bucks or so. It has a long handle so you can do it standing. Wear a mask/respirator and use a spray bottle to wet down anything you might suspect has asbestos in it to keep any asbestos out of the air. Talk to some flooring companies about some adhesive remover.
Others can disagree with me on asbestos removal and even the epa says it is ok to encapsulate it just like lead paint. But I'd sleep better knowing any potentially harmful things were removed from my house. For example, if you found an old WWII bomb in your basement, would you remove it or encapsulate it?