For what its worth, i've had the same issue for a year now. No issues ever arose and it rides fine. I dont normally downplay safety but its $300 you can spend on anything else.
This is just me, but without seeing and inspecting from the inside, its not an apples to apples compare. WE DON'T KNOW the actual condition of the OPs wheel. Heck, some shops MAY NOT MOUNT A TIRE on that wheel. It just depends. OP could be signing a waiver to run that wheel unless the next tire is mounted at home. i.e. if they say "its good" and it blows the side out 4000 miles down the road, thats a no win for all of us.
And I certainly don't want my webAdvice attached to a wheel failure. :shakehead::shakehead:
For $300, buy a new rim and have the old tire mounted and balanced. Save some money by taking off/putting on the tire at home and it should give much better peace of mind than riding around with a potential blowout imminent.