As others have mentioned, the transmission case cannot be repaired. You're going to need to get your transmission re-cased or replace the unit entirely.
Worn-out or broken engine mounts will definitely contribute to this type of failure, but if all this happened while running the car on jack stands and this is the only use the transmission has seen in that car then the case was likely already cracked to begin with.
Also, you need to get your driveshaft shortened some more. The driveshaft should easily install without the need to remove the u-joint caps. If you drive the car with the driveshaft at the current length then the slip yoke is going to bottom out against the output shaft during normal suspension articulation when driving over uneven surfaces, bumps, etc. This will result in damaged bushings, thrust washers, and even hard parts within the transmission. A proper length driveshaft should slide out of the transmission 3/4-inch to 1-inch in order to seat the rear u-joint into the pinion yoke.