To start with, the most important thing is, what was the outdoor air temperature? It’s been cold here for the last few days.
Next, your method of testing for temperature differential is not an accepted industry standard. Temperature measurements should be taken about four air duct diameters from the equipment.
How did you measure the surface temperature of the register? I’m assuming IR. This would not be appropriate for “system capacity diagnosis” of a fluid. A thermocouple is more appropriate. IR just validates the temperature differential is happening.
What was the discharge temperature you are recording? You make no mention of that.
You do realize that there are two heaters in a heat pump system. Raising the temperature two degrees will call in the auxiliary heat. You made no mention of verifying that that was coming on. The auxiliary heat (if installed) has the capability of raising the register temperature to one hundred degrees. The heat pump does not, if there isn’t sufficient heat in the outdoor air.
What are you going to call out in your report? It could be the HVAC equipment, the HVAC air duct system, or the building construction.
There are very simple procedures that you don’t even need any test equipment for to determine if the HVAC is operating correctly. Way more accurate than that newfangled IR thermometer contraption.
Also, a 2 ton should be more than sufficient for that size house in this region.