First - thank you to everyone for the helpful information.

Now some updates. Yes, it most likely would be quicker (and maybe less
expensive) to simply cover the floor with a new high quality laminate
floor - but since I have the time, and the inclination, I'm going to
restore the existing floors.

Also, I tried using heat (as several suggested) to help remove the
tiles. To my pleasant surprise, a heat gun and and scrapper blade are
actually making pretty short work of the job.

The biggest problem slowing me down now is removing the THOUSANDS of
staples in the floor (from where the carpet installers stapled the
padding to the hard wood floor).

Lastly, I need to deal with the glue residue that is left behind after
the tile removal. I'll let you know how that goes when I get to that
part of the project.

Overall, HEAT seems to be a very effective tool to loosen the tiles for
removal.