I'd rent a floor jack or transmission jack,and use a sheet of plywood for a work surface...sure you might be able to bench press it up and in there,but why risk injury or dropping the case and cracking it?...hate to be reading a post here tomorrow about how it crushed your rib cage in...

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You can rent one pretty cheap from U-haul or similar places...
I use my floor jack with a transmission cradle adapter that slides in place of the saddle..its clumsy but much better than trying to lift one in lying under the truck..
When we lacked proper tools at the junkyard,we invented our own...
We had a crappy old leaky floor jack there,that couldn't be trusted to stay up for long.it leaked fluid and would slowly droop, so we hated using it under a car on transmissions,and no room to pump the handle, meant taking the handle off and using pliers or vise grips to pump it up or lower it...it sucked!
I remember us using an old push mower deck with no engine,a peice of plywood bolted over the hole where the engine went,and an old inner tube with another peice of plywood on top of it,to pull and replace a tranny...it was good for automatics ,they had a nice flat pan and sat on the wood without flopping around,unlike manuals and t-cases,
so you had to be careful they didn't tumble off during the lifting process.... it was a lot better than nothing!...had to use a peice of the air hose off an old manual type air pump so we could acess the valve stem to pump up and lower the pressure in the tube to lift and lower the "jack"...(good thing many junked cars had those foot pumps in their trunks!)..
We ended up using a 12V air pump we found in a junk cars trunk to pump it up so we could use it where our compressors hose didn't reach..
It worked pretty good on automatic trannies,they have a flat pan and sit nicely on the wood,but manuals and t-cases were a lot trickier,they lack a flat base and we had no means of chaining them to the plywood...
One day the boss saw us using it,had a good laugh,said "You guys are nuts,what if the tube pops?"...

... he felt sorry for us,and bought a used transmission jack at a auction/swap meet a few weeks later,for 50 bucks...he gave us a lot of credit for thinking of any way possible to avoid "working"...we were more worried about getting crushed by a heavy transmission..

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