Now is a good time to do it! In fact as I am giving up my plot I lifted one of my roots about 2 weeks ago and like yours it has been in the same spot for around twenty years. Unlike yours my two roots were prolific producers hence me fetching one of them home.
When I lifted it there were some rotting sections which I ripped off back to some solid root. As it came apart I found I had two nice pieces each with growing buds so I duly planted them.
Firstly. I dug suitably sized holes and because we have such a dry summer I flooded the base of the holes with water then I lined them with 3"-4" of well rotted manure and placed the roots in place.
Prior to returning the excavated soil I scattered some slow release fertiliser on to it so that it mixed up in the adjacent soil.
Finally I doused the area with more water in the hope that it will water/ filter the soil into any voids that may formed as. I backfilled.
So now it is fingers crossed and hoping that I will be harvesting good crops of rhubarb in future years.
I have attached a section of my webpage on rhubarb growing to back up the comments above;
Week 45-10:
Lift four to five year-old crowns when dormant in preparation for division.
Take care when carrying out this task to avoid damaging the thick roots.
Divide the crowns into sections with a sharp spade, each with some healthy roots and at least one strong bud.
Check for signs of hollow crowns (crown rot) disease and discard all infected material.
Replant the divisions with the growing point at, or just below, the soil surface.
Space plants about 750mm(30") apart for small varieties, and up to 1200mm (48") apart for large varieties.
Prior to replanting, cultivate the soil, remove any perennial weeds, and incorporate copious amounts of organic matter.
I hope this info helps you with your problem....Tg