Does this sound like an undersized heat pump situation?

I just installed a MrCool ducted VersaPro 2K heat pump unit in my 1400 square foot house. Generally I am happy with it but I have some questions. The house is old (1950s) two story and not well insulated which I hope to improve. I think 2K is on the small side of recommended for a house with this square footage, and I knew that going in, but the climate is not very extreme with only about 30 nights below 40F per year. I did not go with the heat booster coil option (HyperHeat).

Just as I gave the system its first test, we were in a cold spell (nights and mornings down to about 35F-38F) and I would see the following situation: the unit would keep the house at set point of 66F most of the night but the on-periods of the cycles would get longer. By the morning the house was not quite at set point (65F vs 66F) and the unit seems to give up and do a defrost cycle. Sometimes it starts up again, stops, and does another defrost cycle. Lots of water drains out of the outdoor unit during this time. The system starts to try to heat again but the lineset tube does not get back to the hot state it is in during good operation, only warmish, and the house never really catches up to set point until there is some warming outside as the day begins. Once the sun comes out a bit and things warm up outside the house gets to set point.

Does this sound like normal behavior for a slightly undersized unit for this job? Any quick suggestions that might improve operation (other than improving house insulation) or to verify correct operation?

During normal heating the indoor unit is showing code 06 or 07, which I cannot find documented. I think those codes mean normal heating operation. (It is not showing EC 06 or PC 06, just 06 or 07.)