275/55R20 is a stock size, I think 275/65 or 275/60 R20s should work.

I think the oem 275/55R20 are plenty heavy myself.

 

The guy at the shop should have measured your clearance, and used a calculator to factor in the new wheel & tire size, then sold you what WILL work. Not guess at what might work. It's all math. If a tire shop guy can't measure how much clearance you have, then figure out what will fit in that space.......you need a new tire shop. That's like a cook who can fry a steak, but never knows how much it will turn out on the inside. If the steak is a little under-done, you can cook it a little more. If the steak is too well done, you could still eat it even if you don't like it as much. But no shop will take back tires you've driven on for a 1,000 miles, only to return and say that you don't like them.

 

I take it you're not planning to add the level? Part of the problem with that size tire isn't the height but the width. 305's are pretty wide in the Nitto. Have you done any plastic trimming or willing to do it? The Nittos are a bit heavy too, but the width again plays a part. Especially if inflation isn't on point.