Ouch, sounds like a typical Goodman fly by night installer. Goodman is fine equipment if installed correctly, but it's a known fact that many hacks install Goodman. Here's the deal with variable-speed air handlers. They actually vary speed to put out the correct airflow. Your ductwork may be deficient, and the blower has work harder to get the right airflow (unlike the old system that just blew at one speed regardless of getting the correct airflow to overcome a deficient ductwork system). Or it could be as simple as the ductwork not being set correctly. You may need another return and more ducts to rectify this issue. Recovered refrigerant should never be used on a new system--you don't know what kind of contaminants it has, and it can be bad for the system. That sends up a red flag. Sorry, this post was in a hurry, but I hope this gives you some direction.

So it has some sort of airflow sensor in it? Cool, I suppose. But shouldn't a 'variable speed' air handler be able to dial itself back to operate with the existing ducts?

Maybe the problem is that he put a 2.5 to 3 ton air handler up there for a 2 ton condenser unit below. This website says that you have to change an orifice for the smaller tonnage or
a TXV.

Would new equipment also need a hard-start capacitor, if a TXV is used?

Here is a link that might be useful: Product URL

No, the AEPF3036 is a rated match with a TXV, and you should be able to adjust the airflow for a 2-ton unit (you'll have to look in the installers manual). You'll have to determine if you need to make adjustments to the ductwork, the air handler, or both... I don't see why a hard-start capacitor is necessary--usually if one is needed the installer should include it.

Correction: "installer" should be "manufacturer" toward the end of my previous post.

Quote from the product page:

"Up to 14 field-selectable airflow settings can be adjusted to optimize the systemâÂÂs CFM for each individual mode of operation"

Apparently, my installer needs to read the manuals.

Here is a link that might be useful: Air Handler Description

Well, I say give the contractor a chance to make it right at least. He may have to do what he said he had to do--add a few more supplies/returns. It's hard to tell the issue, for me, without being there. Ductwork noise is either related to a poor ductwork system or improperly-set blower speed. Good luck.

You may or may not need ductwork alteration but going by your description of this installer I would do nothing on his recommendation, if this person works for a company that has other installers I would call them and get him off this job now

Here is a link that might be useful: Air Conditioning Repair made Easy