The 4L80E will take it when properly built. It is basically a re-design of the 400 with an OD. Unfortunately its an electronic transmission. Until you purchase a tranny and the box to control it, you're looking at around $3000; more for high-torque mods.
The 400 will take it fine but no OD. What I did for the sake of simplicity was to put a gear vendors OD on my 400. It will take the torque, and it has a couple added benefits in my case; 1) if it fails on a cross-country journey in the desert, I can continue without OD, 2) its behind the tranny, meaning it slows the tranny internals down. Not a big issue, but from the standpoint of parasitic losses and tranny life it can't hurt. 3) it was cheaper than a 4L80E and computer. 4) I rarely use it this way, but when towing it can be used as a gear splitter to keep my RPMs at peak power longer.
If you wait a few years, the new GM trannys will be out. Some are out now but I expect them to be expensive and hard to find... translated; they aren't plentiful in junkyards yet. The go by designations like 6L80 and 6L90. They are six speed autos with internal shift controllers, hence no "E" on the name. I assume they still need signals from MAP, TPS, and other engine parameters to run, but the computer is integral inside the case. That might make swaps a bit easier. They use the new bellhousing attachment like LS1s have, so they can be retrofit to older chevy blocks, or BOP blocks with an adapter... or pretty much any block you want since there are adapters out there to put a powerglide on anything. The only difference is that the newer bellhousing is full-round and uses a couple extra bolts that won't be present on your old block. No worries, just leave them empty.
In general, you're looking at some serious modifications. No tranny will really hold up to it, but I suppose a TH400 with about $6000 worth of mods might last a season or two. A planetary transmission is expensive and heavy, but might last a bit longer and you have to put up with things like inability to downshift and often times no reverse.