I think reeds are perfectly happy standing up. As long as they are
standing UP and not LEANING!

We've been standing reeds ( longest are 62" ) vertically since 1976 with no
warping or bowing. I have a sketch of our reed stand at:
http://www.PictureTrail.com/gallery/view?username=billk
It holds nine reeds.
Here in CA, I secure the stand to the wall with a hook, for our little shaky
quakes.

Happy Shuttling ! - Bill Koepp in Central California