Thanks for your reply. I don't have a line wrench, am using a small adjustable wrench, and briefly tried a larger adjustable. The body of the thermostat twists slightly with the force I've applied so far. My 'spider sense' says I'm pushing the limit of what the thermostat body or its mount into the tank can take, but then I can't really see how it's mounted.
The adjustable allows me to basically pull forward (wrench on right) or push left (wrench at 90 degrees to tank). Perhaps a line wrench or open end wrench would allow me to direct force toward the tank (wrench positioned to left) - not sure if that angle would make any difference in how much force could be safely applied. And maybe I can remove the thermostat plastic housing and find purchase for an opposing wrench. Will try again tomorrow...