I wanted to demonstrate that balancing tires on a machine is of little value. You did some measuring and verified the inaccuracies of trailer parts and why there is a need to find an alternative method to bring things into balance. While some suggest using a lug plate on a balancing machine, that doesn't take into account the run out of the lug pattern on the trailer drums. I had one brake drum that needed 5.5 ounces of weight at the usual wheel location to counter the inaccuracies. Had I paid for a fancy high tech spin balancing, it would have still been 5.5 ounces out of balance, possibly more.
While few will go to the trouble of doing it, I'll explain what I do. I have an on-the-vehicle spin balancer, but even that is best only after the following process. I have a spare axle to use for the process, but an axle already on a trailer can be used if the brakes are backed off, or removed, till there is absolutely no drag. This is best done when replacing tires or doing a complete wheel bearing service so that not too much unnecessary work is done.
1. Remove the grease seals and completely clean the bearings, then put a few drops of very thin oil on them. Gun oil or sewing machine oil is fine. Any trace of grease or debris will be a problem. Keep all bearings in their original positions.
2. Mount a brake drum on the axle used for this work and adjust the spindle nut loosely so that the drum rotates freely. The heavy spot on the drum will rotate to the bottom, so there mark the heavy spot, I use a paint marker and use the letter H. You will do this with each drum as its turn comes up.
3. Balance the first drum using small c-clamps or whatever you have. Now you can mount a tire/wheel and find its heavy spot. Again mark the spot with an H, I use chalk. Do this with each tire on the balanced drum.
4. Remove the added weights on the drum.
5. Mount the tire with the H markings opposite each other as best you can, but first mark an S on the drum where the valve stem will be. This will minimize the required amount of weights. Also, it would be a good idea to mark on the drum and wheel where the wheel will be mounted.
6. Add wheel weights to bring the whole assembly into balance, most of the weight should be on the inside of the wheel to better counter the unbalanced drum. If you have the assembly turning freely, you can balance to within 1/2 ounce.
7. Repeat for each assembly. The spare tire can be balanced after step 3 but of course there is no way of knowing where it will be needed, so it will only help a bit.
8. Clean the light oil from the bearings, grease and assemble as usual.
9. Always mount the wheel on the matched drum with the valve stem in the S position.
10. Each person doing all this should add their name to a list below, I expect a very long list. :)