Well POOP!!!

I recently bought a '66 Barracuda 273 180hp with an automatic transmission. The drive train was all in place (I thought), but the car had been sitting for 10+ years. I took all the precautions to start it & see what (engine, trans, differential, brakes) worked. I got it running & pulled it out of the garage to check everything out. I even went through the gears (only a few feet... front & back a couple of times to check the transmission & brakes. Everything seemed fine. While it was idling I heard a funny (OK, NOT so funny) sound & then a BANG followed by the sound of a small piece of metal that hit the driveway. I shut the car off immediately & started looking around for what had happened. It turns out that the piece of metal...about 2" long...is (was) part of the flex plate. It appears the previous owner had not fully bolted the bellhousing to the block (there was a 1/4"...maybe a little more than that..gap). What I need to do now is replace the flex plate & while it's apart, see if there's any other damage. I've never had an automatic trans car before, so I don't know the easiest process. I've got tools, floor jacks, jack stands, a floor-type transmission cradle and & an engine hoist (sadly no lift).
Is it easiest to remove the engine?....the transmission?....both?....neither? I'm open to any suggestions from those of you who have 'been there'. Thanks!