I know very little about Mesa amps, so disclaimer up front.
I found schematics for both the IIB and IIC+, and found significant differences between them. There are a few items which are cursory changes, and could be easily implemented without swapping the board.
However, I assume the "loop mod" refers to changes in how the effects loop is tapped and returned to the lead circuit. This happens at a very different point between each version. The loop is the IIB is driven by a cathode follower, while the IIC+ converts the same tube section to a conventional plate-loaded stage, and taps signal off for the loop from a different stage. Additionally, the reverb circuit taps of the dry signal in a different place in the IIC+.
Looking at it, and knowing both amps are pc board amps, you would enough skill and bravery to not need to ask the question to successfully pull it off. I say that not meaning any slight towards you, but rather because you you need to be willing/able to cut existing traces and replace them with wiring to match the IIC+'s signal path.
There are also some parts value changes here and there, which are less problematic. There may be additional changes (I took a fairly cursory look at mainly the lead channel and the effects loop) that I haven't mentioned. Also, my copy of the IIB has part of the switching for the lead channel cut off in the scan, so I can't be sure there aren't other changes I wasn't able to see.
Shipping is a bear... But if you could ship just the chassis with no tubes, it should be easier. In my opinion, $250 for a new populated board installed is a pretty good deal, shipping aside. If the IIC+ is your dream amp, it may be worth the cost. I don't know what the cost might be to have Mesa simply send you the new board, and have a local tech install it. It would probably be more cost-effective for you, but they may not go for it.