It's hard to know how loose "pretty loosely" is, but one of the reasons the A833 went to the 308 bearing was so that the main drive pinion could be removed from the case without major disassembly. In other words, it's not supposed to be a press fit.
You can bore the case out to the larger bearing, but you'll also need to redrill the holes for the bearing retainer from the current 3.70" to the 308 bearing's 4.16" bolt pattern. If the car's a small block, you'll then have to change the bellhousing as there's no 4.16"-pattern bearing retainer in the needed 4.35" diameter. The only factory LA bellhousings for the 308 bearing are the A833OD units, which use the super-huge 5.125" bearing retainer (also a 4.16" bolt pattern). There are no real drawbacks to that arrangement, in fact we did exactly that when swapping my friend's Charger to a 4-speed. You just need to get the right bell, pivot, and fork as they're all different than the E-body parts. Brewer's Performance can get you where you need to be if you choose that route. You could also use a Lakewood or QuickTime aftermarket bellhousing, which are 4.80" diameter bores and include an adapter ring for the smaller retainer. I haven't used the QuickTime but the Lakewood is a pain in the arse; I have one in my Valiant. The aftermarket parts absolutely require the concentricity to be checked and corrected.
Personally I'd just replace the case. It's probably a less-expensive option than the above. They're not terribly hard to find. I might even be able to scare up a spare if you need one.
Neither option is great if you're worried about numbers for show purposes. In the first case, you'd have the numbers case but the bell and fork will look blatantly wrong, particularly with an aftermarket bell. In the second instance, you obviously won't have the right numbers on the case.
