Not entirely true.. tank pressure will vary depending on ambient temperature and the amount of liquid in the tank. However, the regulator on the tank is designed to allow for the variable tank pressure and provide a fixed output pressure, usually around 11" W.C. The problem is that propane appliances operate on
gas, not liquid.. so how fast the tank can provide that gas (rate of vaporization) is critical. This rate is dependent upon the
wetted surface area in the tank (ie: the amount of liquid in the tank) and temperature (which also effects pressure). As temperatures and/or liquid levels drop, so does the rate of vaporization that the tank can provide.
As for the specific problem.. it sounds as though the rate of vaporization your tank can provide at half full is not sufficient for your Force 10 stove, but is for your cook stove. What are the BTU/Hr requirements for the two? A simple fix for that situation would be to increase the tank size, which will increase your rate of vaporization.
There are other possibilities depending on how your appliances are piped and regulated.. but bumping the tank size up is the easiest to do without any real modifications. You might find a slip neighbor with a larger tank they will let you borrow just to test
Cheers,
Brad
PS: I am by no means an expert on this subject, and hope that others who are will correct anything I've said that isn't accurate. I have however just gone through a fairly extensive crash course on propane due to a completely unrelated incident, and now know way more than I ever wanted to know about this topic.