You're right - the tire load capacity is the bottleneck for payload. Your truck payload capacity will be around 3000 pounds based it's tires and rim ratings.
That's Okay for a small camper but not the larger models such as the big Eagle Caps.
The solution that some 3/4 ton truck owners have found is to upgrade the tires and rims. That will cost around $3500+ dollars. And then you would want to upgrade the shocks, perhaps add a heavy duty sway bar and make modifications to the spring pack.
Your real choices are:
1) Make extensive truck modifications for a larger truck camper
2) Get a smaller truck camper
3) Get a trailer
Or 5th wheel or some other type of RV
Given your choices, I personally would go with the trailer if more than two people are RV-ing in it.