Might be easier to remove what's under the tiles along with it.

What is your plan for the new floor?

Would it be easier to remove the old linoleum too? And then put your vinyl tile directly on the sub floor? If not, maybe a heat gun ($15? at harbor freight tools) might work better than the hair dryer. You could also experiment with other solvents besides goof off. I have noticed that the goof off in the spray bottle seems less potent then the goof off in the smaller non-spray bottles. Maybe a knowledgeable hardware store person could help. Maybe bring a sample of the adhesive in with you and ask them to try different products? Good luck.

Citrasolv is AWESOME for removing adhesive residue. I used it recently when removing a room full of vinyl tile and it worked great. Use full strength with a scrub brush. Then do a final cleaning with a diluted solution followed by a rinse with clean water. I buy it at Whole Foods, but you can order it online. It smells nice, too (made from orange peels). I thought I would need a lot to do the whole room, but used less than two 16 oz. bottles. Did the entire room, by myself, in a couple of hours.