You are making it much more complicated than it needs to be.
Hm yeah I see that. I will consider all my options and then decide which one is the most efficient. Thank you for your help though.
Not only complicated, but then you also have to keep your shaft from moving up and down the threads as well as keeping it in the bearing/bushing.
Another relatively simple possibility if you can use a 3/8" shaft and bearings/bushings is to get the Vex 3/8" shaft tube stock:
Cut this so that it fills the bushings/bearings. Tap a 1/4" thread in the hole (possibly using AM churro screws or similar rather than a real tap), then insert a bit of threaded rod at each end to engage the wing nuts.
I think your best option is to buy a 1/4" ID bearing. Bearing goes on threaded rod.
That said, I also would NOT use threaded rod as an axle if I could avoid it. In my experience it’s often slightly warped along the length. I’d use a bolt instead if I thought I could get away with it, or use @GeeTwo’s suggestion with a shaft. (I HAVE in fact done something very similar because I needed a custom axle. Royal pain in the behind but it works. Would have ordered if I could but I needed too much thread.)
Depending on time/money, however, I’d also look at Misumi. Short shafts with threads on both ends should be no problem. (And it’s cheaper than having McMaster make a shaft for you by a factor of about 6-7.)
Go back to your design: Other than the wing nuts, is there any specific reason to use a threaded shaft? Could you, say, use spacers (like standoffs but without the threads) to hold whatever you’re holding in place? What, er, exactly are you doing–use as much detail as you’re comfortable giving.