Absolutely muzzle down. The cleaning solvents are sometimes not completely removed after cleaning. Over time, they will flow downward. If you store the rifle butt-down, you risk causing damage to the stock, whether it is made of wood or a composite. If you are concerned about the solvent's damaging the cloth interior of your soft-cover (or even hard-cover) gun storage bag, just put a rag at the tip of the muzzle securing it with a baggy and a rubber band. If you have a problem storing the gun muzzle-down because you want to stagger your rifles in your gun case, make sure you put some sort of cloth in the chamber to soak up any excess solvent before it gets where it shouldn't get.
If you are using the Wipe-out foam solvent, introduce it into the barrel from the chamber end and let it foam out the muzzle, rather than vice-versa. There is a YouTube clip on using Wipe-out. If you have a wooden stock, do NOT oil it, or you may risk mushing the stock with oil, causing the action/barrel to move. It may not happen right away, but why take the chance?