I can’t help you on garage height. I’m also not sure about the radius arm clearance of 315s on stock wheels but I can help you measure. The bolt you pictured is a tie rod end on the drag link and it won’t get any closer to the tire if you change tire size.
What size is your current tire? 285/70-17? ( based on google) which is 32.7” Are you staying on stock wheels? (I don’t recommend going to 18” wheels. 17 is a better size for tire availability and cost) Going wider is usually a tighter fit than going taller when it comes to clearance on stock wheels. If you go up to 315/70 that’s like a 35 (34.3) or 1.6” taller so you need 7/8” of height and you’re going wider by 30mm or 15mm (5/8”) out each sidewall. So check your lock to lock and see if you have room to go up and out by that much at the radius arm and swaybar etc whatever is closest. 285/75 is only ~1” taller without being wider but it’s about the same height that comes on non pw 18” trucks
Side note a regular 2500 has taller tires from the factory than a pw despite the power wagon having taller suspension. My Regular 2500 stock size was 275/70-18 (33.1”)
Anyway i have aftermarket wheels but I have duratracs in 285/75-18 which are taller than those options (taller than 35 shorter than 37) and they fit my non-pw2500 just fine. No rubbing through the entire range of suspension and wheel travel. With a 1” level my truck should still be shorter than your truck.
Next to a 37x12.50
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On the rig.
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