From what I found a 3-4" lift will take 31" tires without rubbing. source link: https://www.ford-trucks.com/forums/164125-body-lift-tires-wheels-b3000.html
Maybe you could try 30" tires then? Check your rear shackles and hangers first, I lifted my truck a lot just by replacing the rotted shackles and hangers, also gained an inch or two in the front when I replaced the sagging coil springs.
All I did was level my 05 using torsion keys. I now run 265-75R 16's They are almost 32 1/2" tall. No rubbing
been on for better than a year. No uneven wear.