As a long time owner of a 1946 Bantam T3-C trailer, here are my observations on wheels/tires for 1/4 ton military trailers:
1. 10" wide wheels will be too wide. The tires will rub against the tub unless you have a ridiculously shallow backspacing and then the tires will continually hit the finders. Use a wheel no wider than 8", and preferably no wider than 7". The wheels that originally came with the trailer or wheels of a similar width are actually the best option.
2. Make matching the wheels and/or tires to the tow rig a very low priority. It looks cool, and allows the trailer tires to be interchangeable with the tow rig tires in the even of a tire failure, but the number of times that you will be actually doing that are probably zero. Big tires on a trailer are unnecessary and open a can of worms best left closed.
3. Do use P rated or LT rated tires rather than trailer rated tires. While it may be true that some Discount/America's tire stores won't mount anything but an ST (trailer) tire on a trailer, that is not the case with every Discount/America's tire store. I have had P rated and LT rated tires mounted on the wheels for my Bantam trailer at America's tire stores, also my current military NDCC tube tires.
4. Don't bother with aggressive tires on the trailer. Its doesn't have a traction axle so it doesn't need traction tires. Any AT will do.
5. Don't pick a tire too wide or too large in diameter for the fenders. If the tires are too large in diameter for the arc of the fender you will have clearance issues that will force you to lift the trailer higher than you will like. If the tire is too wide it will hit the fender on every large bump, again forcing you to lift the trailer higher than you will like in order to prevent it.
Through experience, I have found that a 31" tire is the largest diameter that will cleanly fit the T3, MBT and M100 fenders, with 29-30" being better. As for width, keep the tire under your fenders. You don't need traction, and a relatively narrow radial tire will still give you plenty of flotation because the contact patch of radials gets longer as one airs down more than it gets wider.
BTW, this trailer has been the length of Baja California several times and was once regularly used to camp at Glamis and the Oceano dunes. I have used 11-15 Armstrong flotation tires, 11x15 Norseman Tru Tracs , 235/75R16 CJ-5 takeoffs, 245/75R16 CJ-7 takeoffs, 31x10.50R15 and tried 265/75R16. In the end I found that the factory Bantam wheels (4.5" wide x 16" Kelsey Hayes, same as all early CJ's) worked best, with military style 6.50x16 NDCC tires.