Thirds have 5.29's with detroits, dual cases are next in line after bumpers. I have plenty of clearance in the front to tuck larger tires but the wheels wells in my '85s bed look like they might have a little trouble with 37's
Sounds like some trimming is called for. If you want to add a couple more inches I would not jack the suspention up any more. I would use Body lift...2" would be max. Maybe drop the Suspention down 1 and add the BL for 6".
But trimming is maybe the best option.