This jigsaw roller works perfectly for me.
It’s just a piece of felt with an inflatable tube, two straps and a bag but it worked well for me holding my 1000 piece puzzles together.
The felt is smooth, my puzzle pieces don’t snag on it. It’s on the thinner side but is thick enough to stay firm all the way across when rolled up.

The extra large fits perfectly and the rosey matches the interior really well
(a little brighter color but close enough).
The felt material is super sturdy and I’m so glad I now have a way to organize my bag, add some structure and keep the interior clean.
Do not invest in an expensive tote like the Neverfull without this product! It’s a lifesaver.