I have been were you are now several times. I had to install 4. 56's in a 4x4 after installing new wheels and tires. The main thing to remember is this is going to be a very costly expense, and you only want to do it once. With your 37" tires I would go for the lowest gear (higher numerically) possible, which I suppose is the 4. 88's. For some reason, most on this forum and others are afraid of low gears. I don't think they get it, you buy a HD truck with a HD diesel for pulling, and then they order some lame gear like the 3. 54? I know most hide behind the "mileage thing", but the difference is nothing, and if 1-2 mpg is going to break you then you probably should have bought a Toyota. You are asking alot from your truck, it has 37" shoes and as to two. Do you and your truck a favor and go with the 4. 88. You already know how much the larger tires have affected the performance of the truck, so the decision should be fairly simple. The last 4x4 I had switched over, cost alittle over 2000. 00, and yours will be at least that. So plan this thing out now, if you are going to change differentials do the research and and get the one that is right for you. Plan on a front and rear bearing kit, they are not much so change them now. Also there are several good gear vendors in the 4x4 magazines, so give them a call and see what they have to say, what they recommend. the more you do now, the better the swap will go later. Also make sure you have a good drive line shop for the install, if you are not doing it yourself. Good luck and let us know how it went.