it's unfortunate that you did everything right in your research and got someone that did not evaluate your house before the installation. the sad fact is that you may need to move on to another contractor to straighten out the problems.
as the contractor continues to try to bandaid the problems, it gets more bizarre. it's not an isolated story. i hope others will offer comments here. i definitely recommend you bring in another professional.
i will address a couple of issues and ask a couple of questions.
what is the square footage of your house ? this information alone is not enough to size a system. however, if you had a two ton system, more is not always better. in fact, modern technology affords us the ability to scale down sometimes from that approach because the systems are much more efficient.
does the new furnace have a variable speed blower ? if so, it should be able to adapt (somewhat) to the duct static, within reason. the variable speed technology is not designed to compensate for inferior duct design, but it could make the difference in whether it is suitable. usually there are dip switches to select the appropriate cfm of air for the tonnage.
this should be a 2 stage furnace. it could be run on half the heat capacity. combined with a vs blower, this could be a control point. mind you, i am throwing out some thoughts. sight unseen, it's impossible to evaluate.
the issue of heat imbalance between rooms is an airflow balance issue. are there volume dampers installed prior to the branch ducts ? even so, if the furnace is grossly oversized, dampers may contribute to the problem. temperature rise is rated on the name plate. with all dampers open, this reading should be compared with the rating.
based upon the information you have shared, it does not sound like zoning is a solution to your problems. it may only make it worse. if you block off too much air while the furnace is running, it's possible it may shut itself down.
the cfm of air moving across the heat exchanger and the evaporator coil has to be a proper match. of course, the load has to be a match with the equipment or problems like humidity being left behind will result.
i strongly recommend you research and find another company with a well qualified person who can come out and tell you what needs to be done. hope this all works out for you. keep us posted.