several suggestions:

1) Install a ducted dehumidifier, like Therma-Stor or AprilAire. Tie
it into your existing supply duct system and install a separate return
for it.

2) Install the proper size system. No, you don't need new ducts for
the lower air flow. Most duct systems are undersized anyway! Install
dampers on all the branch ducts, do a room by room load calculation and
do a proper air balance using a flow hood, This requires a competent
contractor, with the proper tools and training; only about 1 in 10 can
actually do this!

3) Measure the air flow with a flow hood or another accurate air
measuring instrument. In high humidity environment, you should have
around 350 CFM per ton. This does not mean measuring with the
contractor's hand, that IS NOT accurate.

4) If the system is recent vintage, you may be able to replace just
the outdoor unit if you can get a manufacturer's certified match. The
outdoor and indoor units should be the same brand unless the
manufacturer says otherwise. Then adjust the overall air flow to 350
CFM per ton. Also do an air balance!

5) Do not block parts of the coil, that will cause all kinds of
problems. Adjust overall air flow with the blower speed and dampers.
Blocking parts of the coil with metal can cause uneven evaporation of
refrigerant and may cause liquid refrigerant to slug the compressor.
BIG DAMAGE!!!

6) Seal the ducts, close the windows, provide return paths for all
supply grilles. Opening windows will just allow more moisture to come
in from outside. Installing exhaust fans will do the same thing by
pulling the house into a negative pressure and sucking in outside air!

Get someone to measure the airflow and humidity and quit guessing. And
get rid of contractors who guess!!!!!!

Stretch