OK - you have a few start-up issues. Nobody is always perfect all the time. Especially if they have employees. <g>
But the bottom line is that you still did the right thing going with the heat pump instead of the propane.
My opinion is not a perfect substitute for actual engineering, but four tons of cooling doesn't seem all that far off the mark for a 2500 square foot house in the Carolinas.
And, even if it is oversized for cooling - look at the bright side: it will do a better job of heating.
The conventional view serves to protect us from the painful job of thinking.