+1
I would separate the two if you are working by yourself in the driveway. The T case will make it not only heavier, but will throw the center of gravity off towards the front drive side. It may make everything more difficult to manuver.
I've seen some adapters to a floor jack that will support the transmission and allow you to strap it on. This would make it easier and safer.
2012 Chevy 2500HD ECSB, 6.0L gas, auto, 4x4, LT
2003 F450, 7.3L PSD, 6 spd stick, 2wd, dump truck
1983 GMC K2500 pickup - working on a Cummins 5.9L swap
1987 GMC K3500 Dump, 6.2L diesel, TH400 auto - project plow truck