Have just been looking thru an excellent German Astrophytum site which has photos of nearly every aspect of cultivation. It has a small section on renewing roots on cacti which have either been chopped as yours has due to rot, or have lost their roots for whatever reason.
It has titles in both English and German, and although doesn't really have instructions it's interesting as it shows the plants at the start, and then regrowing their roots at 6 monthly and yearly intervals.

Basically you can see how slow the regrowth is, but that it actually will get there in the end - at 6 months there are still only very small roots, but then another 6 months later it's got a very good root structure, I'd say as much as you'd normally expect anyway. So it's something that will start off VERY slow, but then as it picks up and the plant comes to life again, gets increasingly faster. After being patient and waiting for your plant for a year, that'll definitely be an exciting time for you to see that happen at last!

I'd probably leave your plant on dry sand, rather than moist, as the plant won't absorb any of it anyway and it'll only promote mould or more of the dreaded rot. Given that these photos show that it'll take at least a few months to get even a start on growing roots, it simply won't be taken up by the plant until then.

Hope this helps, Lisa :)