The standard approach to putting wheels on axles seems to be – well – to put the wheels on the axles. The assumption is that the wheels are complete: they have their tyres and crank pins. It’s easy to see why that would be the standard. If you buy your wheels, they naturally have tyres already fitted as that’s one of the hard things that you’re paying for. If the wheels are cranked, then you probably want the crank pins so you can quarter the wheels before the Loctite sets.
In my case, though, the wheels don’t come off the 3D printer with their tyres already fitted, and the keyed axles ensure the wheels are quartered. So, while I’m sure I’ll soon discover why the conventions exist, I’ve installed the wheel centres first. I’ll press the tyres and crank pins on with finger pressure, and affix them with Loctite in a short while.
The crank pins are a nuisance when trying to ensure the wheel sits flat so I can press the axle into the wheel. Normally, wheels with crank pins are pressed on with quartering tools. For #10, I used a jig from GW Models, and for 622 I made my own tool. Percy is quartered with the same keyed axle approach as GTR 1120, but out of habit, I installed the crank pins before the wheels were assembled. I then needed a hole to accept the crank pin in the base of the press.
When it comes to wheel centres, I realized that the distance between them, and indeed any wobble is immaterial. The important measurement is the back-to-back distance of the tyres. By leaving those off until the wheel centres are set, I can adjust them without relying on the plastic centres to have been put on really true or in gauge. Not that I’m cavalier about getting the wheel centres on correctly, it’s just difficult to maintain the back-to-back tolerance mandated by Proto:87.
I shall be very interested to see if this novel strategy works out.
Pembroke:87 
Any thoughts of installing rough-turned tires and then finishing them on the lathe between centers as a complete wheelset, à la prototype? This would give you precise control over the critical tolerances, and ensure that the tires run true with the axle, regardless of any imprecision in installation.
Hi Jeff, Interesting idea. My first response is that it might work with a metal centre, but there is no way one of my plastic centres would stand up to turning the tyre. A form tool places an enormous strain on the part.
But, maybe there is a way to hold just the tyre while turning it in place, then parting off the piece that you’re holding. Maybe you envision a tube that passes over both wheel centres and gets held at the end until the two tread profiles have been turned, and then you would part off all the bits that don’t look like tyre…