Brad,
I sell setups for Cobras all the time....I can answer every question that you have. Give me a buzz...502.759.1431. It's a lot easier to talk than type.
The short and skinny is that I would recommend a TKO 600 with the .82 overdrive (and I may change my mind once I find out your cam specs). You are correct in that it can use the same bellhousing, but the transmission would need a short input shaft installed to fit up correctly. The disc is indeed different. You're going from a 1-1/16x10 to a 1-1/8x26. (You could go with a TKO 500 and not have to change the disc, but the 600 is only $90 more and would give you breathing room in the future if you decide to install a different engine.) The driveshaft shouldn't need shortened if you have a short tailhousing Toploader. The shifter will be about 2" to the right, but I have ways around that.
Also, it's actually the cam durations and lobe separation that determine how thumpy/radical it is. Do you know your cam specs?