For disassembly, sure you could leave the TC on the flexplate. For reassembly, you would have to install the TC into the trans first.
The TC locks on to 3 splines shafts. Each one will allow the TC further into the transmission. 3 steps or clunks. It's a good "rule of thumb" but the best way to know it's all the way seated is to measure the distance from the bellhousing to the mounting tabs on the TC. IIRC, it should be right around an inch in.
Edit: I type too slow. Sounds like a pump problem.
If you want a real rebuild, take a drive about two hours south.