Can I just slip a gasket in place?
First, what’s your opinion on the advisability of cutting the gasket and slipping it in-between the case on the axle and the carrier assembly that bears the end of the driveshaft? After I support the carrier assembly and remove the nine securing nuts there is just enough play to let me get about 1⁄8-inch separation between the carrier assembly and the nine studs on the axle housing. I can feed the gasket over the studs into that space and around the differential gears and position it properly. If I can do this successfully then I wouldn’t have to remove the axle shafts or disconnect the universal joint.
Second, what do you recommend for the gasket sealer? Is grease best or would a Permatex or similar product be better?
Finally, can you give the proper torque value for the nine nuts?
You state that you will “try once again to cure the serious leak from the differential case” so I deduce that you have attempted to fix the leak without success. It is entirely possible that there is something wrong beyond a bad gasket. Damage to the differential case and/or carrier assembly mating surfaces may be the root cause of your problem. It’s also possible that the case and/or carrier are distorted, preventing a uniformly tight fit when they are bolted together.
In light of this, I would not attempt the shortcut you are contemplating. Instead, I would completely separate the carrier from the axle housing, clean the mating surfaces, and then visually inspect and measure them.
There are numerous good gasket sealant products that will help you keep the oil inside your axle. I have successfully used Permatex Hylomar Universal Blue Racing Formula Gasket Dressing & Flange Sealant (Permatex part # 85249) to seal leaking differentials on numerous occasions and can therefore recommend it to you from personal experience. You can buy it at nearly any auto parts store in the land.
Predictably, I could not find “official” torque specifications for your Packard’s differential bolts. I will hazard a guess that a good specification is in the 50-70 lb.-ft. range. The correct torque specification for a given fastener in a given application is supposed to hold the parts together without distorting them beyond acceptable tolerances and without weakening the fastener. You need to make the differential nuts tight enough to hold the carrier in place and tight enough to help create a good seal, but not so tight that you distort the mating surfaces or increase the likelihood that nuts or studs will fail. I think that tightening the bolts incrementally in a staggered pattern until you reach about 50-70 lb-ft of toque will achieve the desired goals.