The 700r4 with the OD top gears is the key to the decision.
4.10's with 35" tires would be marginal on the highway as you simply would not have much, if any, power when in OD. Your gears would be 4.10 x 0.70 = 2.87 equivalent in OD. With 37's OD would most likely be useless. Nobody will ever tell you that 2.87 gears are ideal for the street with this size tire, so why waste your time? My last two trucks have had factory 4.10's and about 31-32" tires with an OD trans and I drove both of them to work on the freeway at 70+mph each day at around 2,500 rpm.
You could live with 4.56's but it would be marginal, not much better than the 4.10's. The equivalent ratio in OD would be about 3.20.
With 5.13 axle gears it would be equivalent to about 3.60 while in OD on the highway, or pretty darn close to your current gearing. If possible get the truck running with the current gears with the bigger tires and cruise down the highway with the trans in 3rd gear (or D....just not in OD) and it would be about the same as the 5.13's with OD. Again, I doubt anybody will tell you that 3.60 axle gears are ideal for 35-37" tires if you had a non-OD trans, or that your highway rpm would be too high.