As far as zoning goes I agree that it probley not needed for your size home. While I did state that I didn't realize the size of your home.
As for taking down the registers to see if that helped in the trouble rooms, I don't really understand what the thought process was for that company to recommend that. Although I might be missing something.
Since your ductwork can be accessed and you have showed them the problem rooms their should be no reason why they can't correct the issues with the temp in these rooms other then just not known what needs to be done.
I wish you the best of luck as I know this can be frustrating thing. Companies saying diffrent things in regards to sizing of equipment, ductwork etc... Again just make sure to get a detailed estimate outlining what all they will do and manual j and d cals. For peace of mind.