I also just leave it flat on the lid, and kept in the bag. I pull slowly to take out film if doing individual rolls. If I need to reroll onto a 100ft bulk loader spool, I also keep both ends flat on the table without the support lids and roll with both hands. With the individual rolls I dont use gloves as I have to deal with taping them onto the cassettes, when I reroll into smaller rolls I use lint free tight fitting white fabric gloves. I have done this with 400ft rolls and 1000ft rolls.
I picked up a set of nice neumade rewinds thinking that I could make it work much faster, but the set I got was for 16mm only and didnt fit the 35mm (the locking lever couldnt engage because of the thickness). But if you have a darkroom, that would be the ideal way, and you can reroll a 400ft spool into 100ft lengths very quickly.