I believe I now know how to flush that cache and will do that, before I change the "A" record to point to the IP of the new server again.....
Hoping MyDomain.com will lower the TTL from 3600 to 300 for a few days, so I can do the testing/migration I need to do a lot faster. -----
Even if your DNS provider lowers your TTL to 300 it doesn't mean other peoples servers (like ours) are going to expire their cache that quickly.
thanks, -Drew