Glove box pops open under mild acceleration

That's not a glove box cover but a Performance Indicator. My first Barracuda was a 1967 4 speed 273 Commando. I knew I threw a good 1-2 shift when the door opened and even better when junk flew out.

IIRC, it did not have a magnet but a spring loaded hinge. My current 68 has the push-button catch. Maybe you could find a 68-69 lid or just add a magnetic catch from the hardware store.