Just went to a known good thermostat/heater combination in another
room, and took the same meter readings.

And got the same results. 240 across line, 0 across load, 120 from
each line to load terminal. Had the stat make, then 240 across line,
240 across load, 0 from line to load terminals.

What that tells me is the meter readings in the bad room are not
diagnostic of a grounded element because a good one reads the same,
but logically it seems a likely place to start.

Except for the fact that it worked fine before the panel was changed,
and doesn't work now. And going around the house i found two more
heaters that don't work, though they don't trip anything. Seems more
and more likely the installer did something wrong, but I'm not sure
what it would be. you don't touch the stat to change out the main
panel.

It's time to turn this over to a pro and see what he comes up with.