Obviously there was something wrong with your heat pump. LP is not cheaper to operate then a properly operational heat pump.
That's what I thought you was saying before, "LP cost about the same as an air sourced HP". That is truely not the case.
It all depends on the relative costs of fuels and how mild (or not) the weather is. (It is hard to beat a heat pump in efficiency until the temperature goes below 34F). On REMC, at $.13/kwh, and at whatever LP was last year, and over the course of "an average" winter, it calculated out that LP was either slightly cheaper or about a wash (I don't really remember which..I just remember coming down on the geothermal side). Now, if you're paying "city" Duke rates, a heat pump would likely calculate out to be noticeably cheaper than LP. As I recall, REMC rates are about double what city folks pay. And your odds of having access to NG is probably greater in town--now it's a whole other set of variables.