Take off as much as you can by shaking, then cut off as much of stem and thick parts as you are able. Then put all the remaining bunches in a bucket, fill some water in an keep it moist (covered). The roots (organic part) will disintegrate (rot). You may add somme effective microorganisms with sugar, or 1-2 tee spoons of nitrogen per gallon (calcium nitrate) to accelerate the process. After 2 weeks or so there will only be perlite and some stinky waste which you can use as fertilizer in your garden. Clean well and sterilize the perlite.

Please note that there is different calibration of perlite, up to 10mm (.40) if I am not mistaken (8mm for sure). This caliber is even better for tomatoes (not for growing seedlings, though) and it obviously "disentangles" much better from root parts. And yes, Hydroton pebbles can be removed even easier.

"Take off as much as you can by shaking, then cut off as much of stem and thick parts as you are able. Then put all the remaining bunches in a bucket, fill some water in an keep it moist (covered). The roots (organic part) will disintegrate (rot). You may add somme effective microorganisms with sugar, or 1-2 tee spoons of nitrogen per gallon (calcium nitrate) to accelerate the process. After 2 weeks or so there will only be perlite and some stinky waste which you can use as fertilizer in your garden. Clean well and sterilize the perlite."

Now that sounds like a very smart solution. I've just tried my own not-so-smart idea with less success: I fished one of the massive root/perlite balls out of the recycling bin, and stuck it in a large tank of water. I was hoping that with shaking, the perlite would sink to the bottom, and the bits of roots to the top. No such luck: about half the perlite floated, and half sank. Same for the roots: a more disgusting brew cannot be imagined :(

Where would I get these microorganisms then, if I were to buy some? What kind?

"Please note that there is different calibration of perlite, up to 10mm (.40) if I am not mistaken (8mm for sure). This caliber is even better for tomatoes (not for growing seedlings, though) and it obviously "disentangles" much better from root parts. And yes, Hydroton pebbles can be removed even easier."

Bigger perlite sounds like a good idea - it's very fiddly stuff when small. Also, Hydroton seems to be twice the price of perlite, and I'm going to be needing a lot, so I might have to stick with perlite whether I like it or not.

I'll fish that clod of perlitic roots out of the bin again then, and try the rot test for the next few weeks and report back. Thanks very much for all the helpful advice!