I have visited Honeywell's site several times looking for a thermostat that has an adjustable timing algorithm which will kick in the Aux heat if the heat pump does not reach set point within the specified time.

However, I have been unsuccessful in finding what I am looking for.

Maybe I an unfamiliar with the terminology used for such a timing scheme.

I would not think that this is such an unusual feature.

What you are looking for is an adjustable differential. That is the item to look for. Now for your problem. If there is not enough swing (separation) in the adjustable differential you will get override problems which compound the issue. When the heat pump will not keep up with the home heat requirements the aux heat will kick in on the second stage. There HAS to be a differential of some sort usually 2 degrees or so to make the glide appropriate.