I remember I also used to have this shallow tupperwear kind of thing that held my palette pad. I could keep it in there for a few extra days other than leaving it out in the open air (oil paint, that is). The only thing was that it was a little bit warped and the lid never sealed/closed all the way, so I eventually had to use it for something else entirely. If I had one that worked, it would have saved some sheets, paint, etc.
I also have little glass jars, incase I mix far too much color, I'll sometimes stick it into the jars with a palette knife and save it.
I like the idea of the double stick tape, and/or the little binder clips. When I'm done with each sheet, I fold them in on each other before tossing em. I could see being able to carrying them around like that without a problem until I got home.