Storing blanket if composed like "classic rubber" blanket - in roll might be ok - still consuming quite some space. If you have polymer stripping blanket with polyester base rolling into small diameter tube, might cause, that polymer layer will delaminate. It makes sense to hang them in rack, apparently, there are hanging systems available. After all, if you are packaging printer and varnishing with stripping blankets, you might have big storage of varnish blankets.
I tried to invent one on my own, but did not realise it in practise - but give me week or two, I will post some idea drawings over here.
Janez