Bummer. Yeah, like to know what the tire size difference is. Yeah, that's a fundamental on any AWD or 4x4 vehicle (Same tire size). Might have 'cooked' the clutches in the Xfer case.
You could always take it to a different shop for a 2nd opinion. Maybe it's not as bad as they say, esp the front diff. Really, the best way to assess would be to remove the front cover off the differential and inspect the front diff gears, etc. This isn't as easy as it used to be on older vehicles. I wouldn't think the front diff would wear THAT much in the few miles driven. I mean guys drive off-road a lot, and in the winter ...and the diffs hold up. But maybe you have larger tires and there is wear from before. For the Xfer case, best is to remove the driveshafts and 'feel' for wear by hand. There's always a spectrum of 'wear' from modest to severe. Unfortunately no mechanic can really 'see inside aluminum' so they can only make educated guesses. The only way to know on the Xfer Case would be to disassemble it and inspect. And even that isn't that difficult to do. But hardly cost effective when you're paying shop labor. As for the engine mount, that's probably just normal wear.
You could always put same-size tires on it & drive it till she gives out. That could be 2 weeks or 4 years. Id be more inclined to think it'll go a while. In the end, if and when it 'goes' it'll probably cost you a good tow off the freeway, but if you're going to replace them anyway(??). Yer probably looking at ~$1,800 or so for used (installed) front diff & Xfer case ..depending on local costs/avail/shipping.
The driveshaft U-joints are probably worn too. Given the age/miles, might not hurt to have the shop pro-actively replace them if they do the other work. How many miles are on this rig?
Summary: A deeper look into the front differential could assess it's gear condition. If that's ok, or minimally worn, then ponder the 'next steps' on the transfer case. Probably best to get the engine mount replaced anyway. If/when it fails, the engine will lift up several inches on the broken-mount side and you'll be driving it, unbeknownst, like that for a while untill something else 'breaks'. What happens is after lifting up a lot, it pulls or breaks hoses and wires, breaks clips, goofs up the exhaust, may cause leaking AC ..and other things that can get real expensive quick. Lot cheaper to fix the MM now than later on. That probably has nothing to do with the diff size tires. Parts wear.