The following is not a cheap solution unless you already have a roll of extra-wide food film, or plan on starting dozens of trays every year.
Plastic food film ("Saran Wrap") comes in 18" and even 24" widths from food supply stores. One roll will cover thousands or perhaps millions of trays.
Or you can laboriously tape pieces of 12" food film together to get a sufficiently humidity-tight cover.
I think the dry-cleaner-bag solution is a great idea!
