Has it been working alright throughout the rest of the season? I had an HVAC system that was incorrectly wired by the installers, so it actually ran the AC and heat pump at the same time, cancelling each other out. Might not be your situation but you never know!
That could be part of a problem if it isn't circulating.
Make sure all the vents are open and not blocked by something inside. Switch filters if you haven't recently, and make sure they are the right kind for your unit. If you can get to your duct work, see if it is leaking anywhere as that will reduce the pressure at the vents.
If you have ceiling fans, turn them on to help out. If you aren't already, close curtains to block direct sunlight (east side in the morning, west in the evening).
I would recommend having a different company check it out since they won't be defensive about the prior work.
You can’t “run the heat pump and a/c at the same time” because it’s a single unit. There’s a valve that slides when powered to switch the hot side with the cold side. That’s literally the only difference between a/c and a heat pump.