Air Conditioning - Need to cool enclosed porch

We enclosed and insulated our porch (best insulated room in the house with the best windows) and then opened it up to the rest of the house. I ran heat in there but didn't get around to AC when work got fast and furious and so did the heat. The plan had been to tap into the plenum in the attic and run an additional duct to a register in the wall on the porch. Since I didn't have time to do that, I slapped a register box onto one of the registers in the living room and ran an insulated hose to the porch, hanging it from the ceiling and the porch door. Not pretty, but I thought it would do the job until I could do it up for real. It doesn't seem to do the job. I get home from work around 11 pm and the house is freezing, because my wife likes to sit on the porch (which is our dining room) and she cranks the AC to try to get it cool enough. So the AC is set at 72 (thermostat is on the second floor) but the porch is reading 79 - 80.

So I got some referrals and the first contractor came out today. His recommendation is for two registers on the porch and to replace all of the flex duct in the house (and the entire system is flex duct) with rigid duct. He says that the increased airflow we would get from the rigid duct would be enough to enable us to use our existing equipment for the additional load. This would also put a damper on each run and enable us to balance the system a bit more effectively than our current system of stuffing a towel in the guest room register when my mother comes to stay. He does think we should look at replacing the compressor and air handler, as they are about 15 years old (we bought the house 3 years ago) and offered a discount on the installation if we chose to do it all at once. I'm waiting for the formal quote, but his guestimate on replacing the duct and adding the new lines was $3,500. What he's proposing makes sense to me, based on my prior research, but I'd like to hear from others that know more than I do. I'm in Northern Westchester, NY. If anyone has a comment on the price based on my region I'd love to hear that, too.

Thanks,
Anthony

There is not enough information to make any kind of accurate suggestion.

The main question first is how big is this addition in relation to the original house?
What you really need is to have a new heat/coll load calculation done and take it from there......................hopefully the contractor that came went to the trouble to do this.

If your existing air handler could handle the added load you would need to connect the duct to the new area directly to the furnace plenum.

Just for clarity, this is AC only - heat is by a different system.
The existing house is 1564 sq ft. The porch is 234 sq ft. So about a 15% increase.
Is a load calculation something you would do before the customer hired you?

The contractor should do the calculation before giving you a price.
A load calculation is what the quotation should be based on.................If none was done then is he guessing?

Actually if you currently have central air and it works well, the increase in the cooling load for such a small addition compared to the size of the house would be quite small.

My suggestion would be to forget the new equipment and duct replacement for now.
Just have either a 6" or 8" flex duct, depending on distance tapped into the plenum at the air handler then split into two grills in the new room.
It would be extremely simple to put a balance damper on this new duct.

Another possibility is to just install a wall or mini split in the new addition.
The problem with being too cool in one room could be handled by an adjustable grill.