Biggest tire on stock suspension

[05 1500HD]

I’ve searched and searched. I’ve read so many different answers. I’ve got a 2014 Silverado with stock 20”lbz wheels that I’m needing new tires. I want to get the biggest size I can without too much modifications. I called a local off road shop today and they said a 295/55/20 won’t rub or a 305/55/20 but those would rub at full turn. 
 

I went to Mavis today to look at the 33x12.50x20 Hercules tt1 tires but they didn’t have it in stock but suggested that I need to go somewhere to test fit that size tire first bc he didn’t think they would fit.   I’m assuming I have the cast UCA’s bc I’ve read that plays a part in the situation too. I have taken the front lower valance off the truck if that matters.