This idea comes up time and time again. I myself used to think it would be the best-of-both-worlds before I learned more. The truth is that these frames didn't change in basic design or suspension technology from 63-87. There is nothing "better" about a newer frame unless yours is rusted out. Sure the very new hydro formed frames are probably lighter and stronger, but not worth the effort IMO (with the exception of the 97+vette frame...
).
The aftermarket for these trucks is so vast that you could upgrade to all aftermarket suspension components if you wanted to and get BETTER performance than new trucks.
The frame itself; if you really want a stiffer frame then box it. One step further would be and X-Member. That's still less work than swapping frames IMO.