Not at all sure what you're dealing with there, but maybe my own experience can help you. I have .75" axles on my front spindles (why would you order only weaker .625" when there's a choice at almost same price), and 1" live axle on the rear.
For spacers on both sizes I just sliced the needed length of spacer off of Home Depot standard .75" and standard 1" galvanized water pipe with my 4.5" angle grinder using cheap Harbor Freight metal cutoff wheels. Wrap a thick piece of (straight edge) paper around the pipe to get a perfect pencil mark for cutting. Very good fit sliding on over the axles, and didn't have to grind down the seams. Where a needed spacer would only be say .375" or less I just stacked washers together instead.
My only spacer needs were getting the front wheels close in as possible to alleviate axle stress without hitting my tierods, and close in on the rear for the axle stress also (stress of curb-jumping etc. increases the further you go out). That's all for the inside of my wheels.
On the outside I had a lot of axle and threads sticking out on all of them, and didn't want to screw my big nylon-inserted nuts that far. I built my current kart with doubled-up nuts everywhere instead of using a single nut with a lockwasher, much less depending on a nylon insert not to loosen. Tightly torqueing 2 nuts together will never vibrate loose within your lifetime, and it also takes up space you would have had to have a spacer for with only a single nylon-inserted nut.
Where there wasn't enough room for me to use 2 of my .875" thick nylon-inserted nuts together, I ordered from BMI some 1" and .75" (they also have others) nylon-inserted nuts (choose the correct TPI) that they label as axle nuts because of the nylon inserts and thin design. They're as thin as a standard nut of that size, and doubled up with any other nut will lock down forever.
You don't have to use spacers or washers where it's too tight, and you don't have to snug nuts or spacers or washers up firmly to a bearing. I'd have the final tighten-down leave enough room to slide a business card through a gap to the bearing before I'd snug up anything to a bearing. Even that old saying about "just tight enough to see a little resistance" when you free-spin a wheel won't be done on my work. Heat expansion, wear, almost anything can cause a little tightening (or loosening) of your carefully snugged-up placements to become too tight, dragging on or even damaging the bearing.
So in the end, my own experiences over a lifetime dictate my recommendation: Use at least a small washer, and if needed a couple of washers or a spacer on the inside of all your wheels after scooting the wheels as close to the inside as reasonable.
Use at least a small washer, and double-nutting with any nuts you want, nylon is useless there, on the outside if there's room. Add a couple of washers or a spacer if needed.
Lockwashers do not go on axles, don't try to tighten anything against a bearing. If you can clearly see wobble in a tire (set up off the ground) at arm's length, it's too loose. If there's any drag or resistance at all in a tire when free-spun, it's too tight.
Remember, "castle nuts" are for the spot on an axle where you have a hole drilled through the axle for a shear pin, to keep a loose nut from letting the wheel fall off or take damage. You can still use them for double-nutting., but they're kind of thick.
Best of luck, think very hard on what you do, safety first, your daughter drives that thing.
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I'm not sure how you can ascertain my mechanical abilities by this post, but thanks for the sarcasm. I'm trying to understand why the factory nut, a top lock without any evidence of nylon on it, won't stay tight, why a generic wheel/tire probably identical to the one that came on this cart isn't fitting right, especially against the spindle, when I should be more or less able to bolt it on with a washer as the operator's manual shows. I've replaced the bearings in these wheels and now it's holding *so far* with a little blue locktite, some washers (though it should not need them) and she's burned through 2 tanks of gas.
