I've just had my engine out and back in after a full rebuild. I don't think there is anyway to remove the transmission without a) removing the engine first, or b) removing the engine and transmission in one assembly. Splitting the engine from the transmission in the car is easily done in less than an hour (remove starter & bolts (3 of), remove flex-plate nuts/bolts while in neutral (6 of) and bellhousing bolts (6 of). Make sure the torque converter stays in the bellhousing as you slide back and remove the engine.
I would suggest if you are on your own then remove the engine then the trans for "ease of handling". I used a 2-1/5" ton engine crane just to get enough reach beyond the front bumper
and into the engine bay. You'll need to remove the radiator (4 bolts and two pipe clips, easy job) and fan assemble but not the hood if you are careful. I made a special low profile lifting clamp when I removed my engine but its probably not really necessary.
If you instead plan to lift the whole assembly on one piece then remove the hood, radiator, front grills and all the associated framework which will make extracting it much easier. Someone once posted the framework would take an hour to remove but I'd say more like two or three. I would say going this way is much more extra time and hassle than splitting the engine from the transmission and lifting out in two parts.
From your description the leak could be from the torque converter seals that ride on the transmission input shaft (quite easily changed after sliding off the torque converter to gain access to them, note there are two drain plugs on the front flat face of the torque converter) or from where the input shaft enters the transmission.
Hope this helps.
Last edited by Mark Norris; 03-11-2020 at 02:13 AM.
Mark Norris
C56G3186
1963 Aston Martin DB4 Series V Vantage
1951 C-type Jaguar (alloy replica)
1934 Lagonda M45 Tourer