A few months ago we moved into a rented house that uses a propane
tank for heat, and the owner isn't willing to replace the piloted stove/
oven combo with one that isn't sucking up propane 24/7 (at $3.50/
gallon). We've adjusted the pilots best we could, but we can tell by
the amount of heat that a lot of energy (and $) is being wasted. The
owner won't even allow us to replace the unit at our own expense!

Short of shutting off the valve to it entirely, and losing functionality
(practically speaking) of a stove/oven, do any other options exist?