Makes more sense. Thanks.

I am going to guess that being kids their doors are always closed. My kids closed and locked. Doors are tight to carpet with no air flow underneath. Could be part of problem.

To balance the air when it is installed. After it is installed and correct there would be no need for closing or opening any.

I had a similar thermostat placement to yours. In my house, that thermostat and return vent serviced the living room (behind the camera). The bedroom to the right had a separate unit blowing into it. The cool air in the bedroom was forced through the door into the mini-hallway with the thermostat. The living room would be roasting every time the bedroom unit kicked on.

The wiring for the thermostat would have been too difficult to move it, so replaced it with a remote thermostat where the temp is read at the remote.

It's a thermostat placement issue, never shut off a vent. That's why you have space under your doors. If you do, you're putting more load on your unit

What is the air flow like? Do all your rooms get about the same pressure flow? Is it a longer run from the unit to the cool/hot rooms? There has to be a way to redirect things up in the attic. We have a similar problem and need to do the same. Daughter's room is cold in winter and hot in summer.

This !!!!

Ducts coming off the cap end of the plenum get the lion's share of airflow. If you are trying to regulate airflow at the outlet registers that would be wrong. Dampers should be at the beginning of each INDIVIDUAL duct run. Obviously the correct move would be get a qualified duct man (or 2) to look at it and get their opinion and a bid. I would not start out telling them the plenum needs changing ... just tell the the temp problems you're having and see what they come up with.

The t-stat needs to be located as near the return ait as possible to sample and react to house temps not just a section of the house.

Why is there not a stat for each damper? Useless dampers without it.
If your damper does not have a control reference, then it is relying on air balance. You need to have the airflow balanced by pinching off registers untill you have the correct flow to each space. The unit needs the total airflow to match design., but where the air goes is determined by closing off registers. Anyone who tells you different does not understand air balance.
After saying all this, if you do not have sufficient (Design) flow with all registers wide open, you will affect efficiency closing off registers