I started to do some segmented bowls to empty out the flat scrap bin. To get the rings flat, I made a large MDF disc that goes on my face plate, attached some hook (and loop) to it. I then put some 4” klingspor paper on it.
Questions.
The paper eventually catches at the seams between strips during sanding and lifts. I’ve ordered some actual disc paper but I wonder if there are any tricks for making the adjacent strips of paper work?
Are there any jig ideas for bringing the ring to the sanding disc other than just holding it there with my hands? Through carelessness I let one slip and broke apart the segments. That lesson has been learned! I sort of imagine something where I can attach the disk to the tail stock and gently move it to contact the disc.
I see little tables that ride the lathe bed but that wouldn’t work for something as tall and narrow as a ring.
Without more info, some questions and perhaps ideas based on guesses...
What diameter are your rings?
What grit are you using?
What is the swing on your lathe? (i.e. can it swing a sandpaper disk large enough for the an entire ring?
I have a standalone belt disk sander and use 10" adhesive-backed sanding disks. However, a quick search of Amazon showed larger disks - I saw some 24" in diameter in various grits, for example this in 100 grit:
Do you use any support or are you holding by hand?
I see Best Wood Tools offers a 4x12" steel table that attaches to the lathe banjo. If that would help, you might call for info. (Their website is sometimes not too useful)
If holding by hand and that's difficult to control, I'm wondering if it would be easier to make some sort of jam or Cole-jaws type of adapter to hold the piece from either inside or outside to keep it straight. This could be mounted on a live center in the tailstock if the rings were smaller diameter than the sanding disk.
But if the rings could be mounted and spun on the lathe, could they be flattened with a scraper?
I too use a drum sander (Performax 22/44) but my place would be a long walk from where you live! Are you in a woodturning club or know anyone in a woodworking club. Many have equipment and are willing to share.
Also, a friend took a glued-up table top to a local cabinet shop and they ran it through their big sander - don't know if they charged him anything.
Also, I have a roll of coarse grit sandpaper, maybe 18-24" wide (can't remember). I may have gotten it from a bin at Klingspor, can't remember that either! I've occasionally torn off a piece and taped it to my workbench and used it to flatten things - pushing across the paper by hand. Worked well but not real fast.
Also, for glueups (not for segmented but solid wood for Beads of Courage boxes and such), I've had good success by holding a big sanding block against the face. I glued some 2" wide coarse sandpaper to a fairly long 2x2 (using spray adhesive) and hold it against a surface while turning the wood at a low speed.
The pieces I usually use are like these, about to be glued together

Of course, these already have a way to attach them to the lathe! But if you used something like cole jaws or perhaps double-sided woodturners tape to attach a ring to an MDF disk in the lathe, a big sanding block might work. With coarse grit it's surprisingly fast to flatten a layer.
JKJ