Your biggest issue with a frame swap is going going to be the track width like Hot Rod Lincoln mentioned above. Pretty much everything with "truck" weight capacities post 1955.2 are quite a bit wider and the tires will stick out past the fenders. It is a look, but not one that appeals to me. Being illegal is also a pretty significant downside.
The weight of an LS/4L80e will be a bit less than your current drivetrain. I don't know enough about the front suspension setup on the AD trucks to say if there is an easy fix for that. Maybe someone with more eperience on them can chime in.
In terms of mounting the engine, I you would run into issues with the frame width since the earlier trucks were narrower. You can work around that by raising the engine (the LS is shorted than the I6), but then you run into clearance issues with the transmission tunnel.
All of this is solveable with enough time and effort, but it is a non-trivial amount of custom work. Generally speaking I am all in favor of a good swap, but you need an idea of what you are getting into before you commit.
On the subject of picking a donor, the the 1999-2002 engines use a 512k ECU and (almost all) have a cable throttle and mechanical fan. The 2003-2006 use a 1mb ECU and (almost all) have an electronic throttle and electric fan. There are other differences in the wiring, with the later engines having more sensors (such as the oil pressure) wired into the ECU to enable additional diagnostics. Once you get into 2007+ engines, you get the Displacement on Demand and Active Fuel Management versions and lose a lot of the reliability.
I personally like the 03-06 versions best. The electronic throttle pedal is easier to retrofit into random place, the electric fans are lower profile than the mechanical ones, cruise control is free (built into the electronic throttle system), and the electronic throttle works better than the IAC for getting a larger cam to idle smoothly.
