This is the swap I did into the coupe. The TKO600 will slide right into the 606 belhousing, no issues with input shaft stickout. I recommend you use a roller pilot bearing. The rounded edge goes towards the trans. You can use the back side of a matching-diameter 1/2" socket if you are careful and don't smash it sideways. You may need to lightly sand the hole in the crank to clean out any crusties.
The Tremec instructions specifically say to check the bellhousing runout with a dial indicator. I had to pull out the block dowels and install some .007" offset ones to get it just right. Ask if you need advice on how to do this.
With the 606, you are limited to a 10-1/2" clutch on a 12-3/4" 153-tooth flywheel. This is adequate, just get a decent clutch kit. If you are serious about power, then the cast aluminum GM bellhousing won't save your legs from a clutch failure - a steel safety bell will, and then you can go to a 14" 168-tooth flywheel that will support an 11" or 12" clutch.
I replaced a 700-R4 trans with the Tremec - the driveshaft was really close in length although I had to swap the yoke, as the Tremec uses a Ford version - just need to pick up an adapter U-joint at the parts store - GM on one set of caps, and Ford on the other. If I recall, the driveshaft is about 3" shorter than the OEM one used on a TH350, but almost the same as the one used with a 200-4R.
I used a Jegs dual-hump crossmember for the 700-R4 - I had to trim the top/front edge of the center section (just welded a strip of 1/8" plate back on and repainted it), since I did not want to modify the tailhousing of the Tremec. The trans mount pad matched up perfectly.