I did a tire, wheel & level kit upgrade last year and went with 285/75R18 tires. I chose those as they gave me the height I wanted on the front.
Here are a few pictures showing the differences between a stock 275/70, a 295/70 & the 285/75 size I used. The comparisons provide dimensions and speedometer errors that may be useful to you.
I don't know if you'd see rub with either of the larger sizes without a level kit, but I suspect you won't.
275/70 vs. 295/70:
View attachment 95391
275/70 vs. 285/75:
View attachment 95392
Here is my truck stock, then with the tire, wheel & level kit upgrade.
Before:
View attachment 95394
After:
View attachment 95396