Congratulations. I've been to NOC and it's a nice area. That drive across Cherohala Skyway is awesome, and of course the Great Smokies NP too.
Be glad you have a 360! We had a '71 that offered only the 318 and I don't think it had much more torque than a Slant Six. Don't try for "More Power" by stuffing a Big Block in there. There were three front cross members. One for Six, one for Small Block, and later one for Big Block.
Your transmission is probably in the TorqueFlite "727" series. Dodge called it LoadFlite for trucks. There was a smaller "904" series that I think was mostly used behind six-cylinders.
But! Not all 727's were the same! In the truck application, they used beefier gear sets and I'm not sure what all else.
Two other warnings:
1. If you replace the Torque Converter, it has to have a Balance Weight and a staggered Flex Plate so it only mounts in the balanced position. It also must be for a TRUCK/Heavy Duty application! Needs to have a LOW Stall Speed. If you use a High Stall converter from a performance car, you'll have an RV that can burn rubber off the line, but it'll also burn transmissions because the converter will still be slipping (and creating tons of heat) at road speed.
2. We lost a good-working 727 because the cooler in the lower radiator tank failed and let antifreeze into the transmission fluid. I installed an external air-over cooler and did not run the fluid through the radiator cooler at all. Just be sure that aftermarket cooler is a large one since it's handling the entire cooling job, not just helping another cooler.