The stat seems to be OK. I was afraid that the relay got stuck, but your description shows it's not the case.
I once had a similar problem. The 1st tech suggested to replace the igniter and ordered the parts for me (~$40, labor extra). The 2nd tech came with the brand new igniter, but didn't install it -- he said igniter rarely needs to be replaced. He found out that the igniter cable was not making good contact for some reason. After replacing the cable, the system has been working fine ever since. Just a big FYI.
Normally the HVAC tech will not fix the circuit board. They don't have that knowledge. I'm surprised that they don't have a spare board for you to test first. Is your system old or rare? The replacement part for discontinued system is more expensive. But still $500 seems to be a lot of money for a circuit board. Can't they look for a used part recycled from the old systems they exchanged out?