This is something I have spent a lot of time thinking about. Before I say anything further I have to throw out the fact that I am NOT an expert and don't know what I am talking about. That having been said...
When thinking of long term storage I don't want to put straps in plastic. Long term I just think that the chemicals used to make plastic might affect the notes down the road. There are "safe" plastics for storing individual notes, but straps are a different animal.
Here's what I think is best. Take 2 worthless bran new notes and put one on the front and one on the back of the strap to protect the notes you want to save. Then I put them in paper, such as a heavy envelope. I lay them down for storage and try not to put too much on top of them.
I think even pressure is important if you do set something on top of them. In other words a level base and don't lay something half on top of them. If they are stacked, stack them even.
I would actually love to hear from other people on this subject as you may have better ways of going about this.