Fabric Turner (version 5)
Couldn't find a design for this on thingiverse so I decided to take a stab at making one myself. I haven't printed this myself yet, but I will try soon to test it and add photos/videos of it in action then. Version one was chaotic, and skipped all the way to version 5 before I found one I like that is easy to print.
For smaller tubes, scaling it down should work fine.
Instructions for use:
Slide inside-out fabric tube over the outside of the turner tube. Then, grab end of fabric with "pencil" shaped pusher, and push through inner tube. Grab the top of the fabric once it peeks through the end of the tube and pull it all the way through to finish turning tube.
Bonus tip: Use the "pencil" as a corner pusher to pop out those pesky corners without puncturing the fabric.