Well, the first thing that came to my mind is the 1/4 or 1/2 inch Baltic Birch plywood. It is much thinner and not heavy at all. You can find large sheets of it at Lowe's. It is not too expensive, and it is very smooth.

Is the mural wallpaper? What is it attached to now? Make sure that it will fit through all openings on the way to the 3rd floor too.

Good luck with your move.

Luvs

I'm wondering if that white fabric sizing that you use to stiffen thin material would work? It has a glue like substance on it & using a dry iron it adheres & stiffens to the back side of material. Can't imagine why it wouldn't work on a mural. Then, you could get the decorative, primed molding that comes in 10' or 12' lengths & have it cut & mitered and nailed into a 'frame'. Once in your new place-simply staple the mural to the back edges of the frame and add the saw toothed brackets along the top to hang it. Another idea is to get 3 yds of 60" wide cotton fabric and several bottles of liquid starch. Dump the starch in your bathtub, soak the cotton thoroughly, then wring the excess out. Then with the mural on a flat surface like your flooring-(have someone help you..) lay the cotton on the back side of the mural & using a flat tool (paint scraper/trowel?) work from the center & smooth it out to the edges of the mural. Use pinch clothespins to hold it in place..LOTS of them..and hang up to dry. Overnight it will stiffen like magic. Messy job but cleanup is easy-soap & water!