It isn't the wheel width, it's your offset. 33" tires will clear by 2" in all directions unless you get an offset that hangs your tires halfway out of the fenders.
Engaging MTS would have worked also. But yeah, having a front tire and rear tire slip at the same time is relatively common when off roading, especially in mud. It's the reason I roll my eyes when people purchase the non-Off Road models to throw big tires on and play make believe.
Turn this shit off in the Toyota app if you haven't already, because Toyota reports everything you do with your truck to your insurance. After turning it off, you should get a letter in the mail verifying that you turned it off.