I'm following the guide here: https://www.amclassic.com/pdfs/17mmHubOverhaul.pdf to service my rear hub. Problem is, I can't get the inner (adjusting?) nut off! The outer (lock?) nut came off just fine, but when I try to unscrew the adjusting nut the axle turns with it and I can't figure out how to keep the axle still...

Watch out for that link above^^^. It wouldn't load, giving me a frozen screen. Couldn't close it - had to reboot to get out.

Good grief, it's just a PDF file. There is nothing wrong with the link.

Maybe not - but that's what happened to me. Mileage may vary.

Can you get two nuts on the axle above the stuck one? If so, thread them on and use them as jam nuts, place a wrench on one and use it to hold the axle still while you loosen up the stuck nut.

BTW, the PDF opened just fine for me.

Put a wrench on the flats at the other end of the axle to hold it in place while unthreading the adjusting nut

Do you have the other end of the lock nut (the other side of the hub) on a vise or a another cone wrench or something that holds it?

nut/cone ------axle:hub-----cone/nut

so the cone you are trying to take off on the right of that diagram, you have something holding down the left side?

There's nothing clamped on the drive side - nothing to clamp it to, really.

It doesn't matter, I just kept turning the two nuts this way and that way until they came undone.