This is an interesting swap. Transmission wise I would stay with a strong rebuild of what you have to keep things simple computer interface being the primary consideration. Another issue that you will deal with is the Intake/Injection system programming to deal with the added cubes and cam timing of the 383.
Before you commit consider this: Check the Houston/Sugarland area salvage yards for a LQ-9 6.0 and Transmission set up from a scraped 2003~2006 Escalade/Denali. Get the whole shebang..Engine/Transmission/Computer and Accelerator Pedal assembly. There are plenty of guys on line that have done this swap with 90's model Chevy/GM pickups that should be similar to the Tahoe. I have seen this done to a '97 4 door Tahoe and with no other mods than intake and exhaust...the truck was a real screamer. I have seen the entire package I'm talking about occasionally here in SE Florida on Craigslist for around $3500 with less than 75K miles....Lot of bang for the buck !!
Example:
https://miami.craigslist.org/brw/pts/5475916185.html
