The 360 will hold up fine. Its more of a transmission and axle problem you're looking at. The D44 doesn't do 35+ very well. 4.88 at the very minimum for 38s, 5.13s would be more appropriate though. That is if you like not replacing transmissions.
As far as turboing goes, factory bottom end will take nearly 20psi and 700wtq before it blows on e85 if your tuner is worth a damn. Factory heads will tend to lift once you approach 12psi, 12 and past will require headstuds.
The real problems and cost that comes with turboing comes in the fabrication required. You will need:
-fully custom fabbed headers to run the turbo
-fab hot side piping
-fab intercooler mounts
-fab cold side piping
-blow through carb hat that will hold in place under boost
-255lph fuel pump
-larger injectors
-sct tuning (FlyinRyan is the man)
-wideband 02 gauge and sensor
-run oil lines
to name a few things.
Much as I hate to say it, you're better off with the cummins. Being as your truck is your family daily and work truck, I wouldn't **** with all that fab work. Now if you're just going to have a shop do the work, prob won't be down long then and its a possibility. Cummins you could hop right into, have the beefier axles for 38s as well as lower gear options (5.13s and up, d44 ends at 4.88).
There is another option that I don't necessarily suggest but there is ways to improve it. There is a company called P.I.E (Performance Injection Equipment) that, if your pockets are deep enough, sells kits to turbo these engines or mount a vortech centrifugal supercharger on instead. The reason I don't necessarily suggest these guys is because they've been known to build 408 engines for customers that begin to knock shortly into their use and their in house sct tuning blows up motors. You COULD buy their hardware, install it yourself, and get tuned through FlyinRyan and probably have a decent setup.
