Is the detuning happening just on the top heads? If so, you may be right. If there is force against the head by gravity pulling against the rim-attached mount then seemingly all you need is the vibration created by just playing the drum to gradually loosen the tension rods. So your idea may be worth a try, especially if it keeps you from having to use those pain-in-the-ass lug locks.

Tim has posted some good tuning info here...maybe he'll have a suggestion.

Yeah, I know what you're saying about the floor toms. It could potentially bend the mount, I would think....?

It would take some time to do, but if all else fails, get new tension rods of a different brand but same length and get the little floating rod receiver for each new rod, too. The rod receiver is the short tubular nut that goes inside the lug casing. So you would have to take a head off and remove a lug to install new receiver. But try a different brand, because maybe the Premier's have more a tendency to slip (I don't know that for fact, but possible). You could try replacing just one or two that have slipped the most, then see if the problem remains, or goes away with new rods/receivers. Make sure the replacements are as close to the originals in size and dimension, or the receiver may not fit snuggly in the casing.