First we need to find out what all the problems are. It does not hurt to over size a furnace. Some of these guy will tell you anything because they don't have the nohow to find the real problem.
The furnace you have has a blower in it that can move about 1,600 CFM of air if ducts are done right. Here are some things i need to know to help you check out the engineering.
How many hot air opening do you have?
Are most of these opening 6" round pipe?
What size are your hot air ducts leaving the furnace?
What size is the return air ducts?
What size is the filter?
How many 3" ells are on your stack.
How long is your stack?
It would really help if you could take a bunch of pic. so i can ask more question.
Answering these questions and taking the pic. is the best way if you want me to tell you what all you have wrong.
There is nothing worse than having a heating system that don't work right.
What size is you air con? Take the model no. of the outside unit.
There might be a few little things we can do to help your problem
Just like you were talking about you filter being part way out to keep it off
limit. No more than 300 CFM of air should go through 1 SQ. foot of filter.