Tire size question w/stock 20” wheels: Keeping rubber inside the wheel wells?

[Big Bend Brian]

Looking for advice: I have a tire question that I bet others would be interested in seeing answered too. First, I’d like to say I’ve learned A TON ton of info from you all regarding the new 6.7 Super Duties (thank you!). You’re enthusiasm is contagious and it made my decision a lot easier to get rid of my 25 yr old daily driver (Toyota 4 Runner w/260K miles) and replace it with a new F250 (this will be my 2nd diesel as I still own and will keep my 2003 7.3 Excursion that just hit 101,000 miles).

Twenty eight days ago I ordered a 2012 King Ranch F250 in Golden Brown (FX4) with LT 275/65R20E tires, 20 inch Chrome Clad Cast shoes, and a 3.55 E Locker.
1) My question is what larger size All Terrain type tires can I go to, while keeping the stock KR 20” wheels, that will give me larger tires, a wider foot print, and hopefully a noticeable higher stance but will not have the tires extend outward of the wheel wells?

Upon delivery I plan on immediately either having my local 4 Wheel Parts shop level it with an ICON leveling kit or put on an Icon 4.5 inch Stage 1 Suspension kit ($1969)-thereby keeping my FORD warranty valid too (Ford Authorized modification company in my area). I’m still undecided as to which I will do.

2) Having larger tires on stock 20” wheels will probably not look odd with it leveled but would it look odd/weird with a 4.5” lift?

Based on a lot of your forum information AND photos (thank you again) I was planning on putting 35 x 12.5 Toyo M/T tires to go with the 4.5" ICON lift kit and 20 x 9 KMC XD Armour wheels but I’m not sure I like the look of having ~ 2inches of rubber sticking outwards of the wheel wells (I don’t want to put on fender flares).

3) Not being a tire guy is it possible to have 35 inch Toyo M/T tires on 20 inch rims and not stick so far out of the wheel well?

I will not be off roading but will hunt with it and I’ll only be pulling boats up to 8k lbs.

Brian