I'm not suggesting you can't install it yourself for much less. But what it cost an individual vs. what it cost a retail establishment are 2 different things. You can change your own oil for $75.00 bucks or so a shop will charge $150.00 or so. That doesn't mean the shop is over charging.
When calculating your 2 hour time make sure you include all your time. The time you spent getting model number off unit the time spent ordering on Amazon. Did you do any research on the unit or did you just buy the cheapest thing you saw? Did the unit go straight from Amazon truck to your roof or did you spend time unloading and storing first. Did you get unit on the roof by yourself or did you need help.
A shop is most likely buying equipment from a wholesaler and not the cheapest unit they can find on Amazon.
The shop is also marking up the unit. They are not selling it to you for what they paid!
It will likely take a shop 3-4 hours, but start your clock from the point the shop moves the unit from the yard to the service bay and from the bay back to the yard. Once the unit is parked and ready for pick up you can stop the clock, Make sure you figure to pay not only the tech that actually did the job, but pay the person that received the A/C unit, the service writer, the cashier and the fork lift jockey that moved the unit. Lastly the shop didn't just put your old unit out at the curb, they paid to dispose of it. Hopefully the freon in the old unit didn't require a hazardous waste fee.
I won't get into overhead like utilities, insurance taxes etc. I think you begin to get the picture.
A individual is not doing the install for profit the shop is and charges accordingly!