"Or rather, I may have the capabilities but definitely not the patience!"

Joining these beforehand would've been simpler, faster and less demanding of your patience. It looks like the basic options have been outlined so you can take your pick. Prying the misaligned piece out and scraping it seems risky. It might result in something even more unsightly. If you have more of the strips you glued up with the pinstripes, you can just carve, scrape and sand off the misaligned piece and replace it with new.

If you do mess around with the heatgun to loosen the glue, try warming it repeatedly for brief periods. The surface of the wood will heat up and discolor faster than the interior. Pulling the heat away and reapplying in "spurts" allows the exterior temperature to rise as gradually as the interior. Soaking it with water beforehand would help a lot but I can't see how you might be able to manage that.

I hope it works out. It looks cool!