It costs me around 250$ where I live to fix a 2nd gear synchro. I don't understand why it would be so expensive in the US.
I have a bad synchro as well. If I'm running high RPMs on 1st gear and tried shifting it into 2nd it would grind like crazy and has a terribly hard time shifting. I just skip 2nd gear now and shift from 1st to 3rd except if I'm at really low RPMs where the problem wouldn't occur and it would shift normally into 2nd (although not as smooth as before).
EDIT: Congratulations on the new build! I envy you