Let's stay focused for the moment...the moniker of "WorryWart" is becoming way too appopriate.
When you did Bill's experiment of shutting down the outside unit but allowing the indoor blower to run, did the noise complaint you have go away, or did it remain?
If it remained, it's an airflow issue. If your ducts are all metal, and all of them are externally insulated, the inside surfaces of the ducts are hard and are transmitting the blower noise all over the house.
I just learned that your old system was a gas furnace. Gas furnaces typically are not as loud as air handlers. With a gas furnace, the blower is on the bottom, then there's a heat exchanger, then there's an A coil for cooling the air in summer. Above that is a plenum, where the air then goes to all the ducts. With a gas furnace, the air patterns are much more baffled coming off the system due to this chain of components.
With your heat pump air handler, the cooling coil is on the bottom, and the blower is above it. Past that there is not much in the way to baffle the blower noise.
To serve as an example, my own house has a gas furnace, with cooling coil on top, and a sheet metal plenum that goes into the attic, where round sheet metal ducts take the air to all the supply vents in the house. I do not have obnoxious sounds coming out of my supply vents. A quiet rush of air, far from annoying or distracting. The loudest part of the system is at the return, and even there it is tolerable.
Your other installation concerns raised by my colleagues here are valid. That being said, to correct your original complaint, you may be in for additional modifications to your duct system, since you now have a different type of equipment moving the air.