Jono,
I can't say I have a complete answer, but I do have a few suggestions for troubleshooting (at least, where I'd start to tackle the issue).
The first thing I'd do is determine confirm that the system is actually in heating while the thermostat is trying to hold the cooling setpoint. The hourly report block for the system has two output variables - "Total central heat coil output" and "Total central cool coil output" that represent the heat added or extracted by the central coil. Since your system has only one coil, at least one of these two values should be zero at all times. Another thing to check is the "Current hour heat extraction rate" in the zone report block. It's been a while since I've looked at it, but I believe if that value is negative the HVAC system is heating the zone (and positive if it's cooling). Though I'll have to warn you that my troubleshooting methods sometimes raise more questions then they answer, so if you follow these suggestions you automatically agree to my indemnity clause...
One more thing I'd consider is if the HVAC system is really appropriate for the application. The Packaged Variable Volume system (abbreviated PVAVS in eQuest terminology) is really more of a VAV system with DX cooling in place of a chiller. If you're really setting up a system to serve a single zone, then Packaged Variable Volume Variable Temperature (PVVT) or Packaged Single Zone (PSZ) might describe the actual system better. eQuest help also has descriptions of each of its system types in its help library, which you can find by right-clicking on the "System Type" pulldown in HVAC system box, navigating to "Topic Help", and picking any of the Air Side System Types options that show up. (You might already know about this, but just in case.) I've found these system descriptions really helpful when I'm trying to figure out how different systems are controlled and how they respond to zone demands.
Good Luck!
Drew