Robert - After doing a bit of research and comparing your side cover shifter detent spring (1st pic) with the one pictured in an original side cover (2nd pic), your existing spring in fact looks to be the incorrect size. I searched through available Shop/Service manuals and parts books and can find only 1 spring for the Saginaw 3 speed (also fits the Saginaw 4 speed too) called for. Nothing shows a different strength/style spring for the OD equipped 3 speed.
Armed with GM# 3831718 - Spring, detent cam (3rd pic shows applications from parts book), I searched a bit on the web and actually found some NOS springs being offered. The pictured NOS springs (4th pic) are clearly much stronger, with very little hook end lengths and lots more tension coils than your existing spring. Just my $.02 worth on this, but get you one of those NOS springs and give it a try. I think it may solve your popping out of reverse dilemma.

PS: I posted the links to a couple of NOS spring ads in your
Truck Parts Wanted ad.