Hey Gzgirl,
The condensation on the brownboard is accumulating because warm, moist air is contacting a cold surface. This causes the water vapor in the air to condense or turn into water. Just like the beads of water that form on a cold glass of lemonade on a summer day.
You're contractor straight out lied to you about the insulation and now you can visually see what's happening. You're losing tons of energy because the air inside the ductwork is losing its cool as it moves from your A/C unit to the rooms in your home. This cold energy is transferred to the brownboard.
In the winter, this reverses and the hot air from your furnace turns into luke warm air as it loses some of its heat to the brownboard and outside air.
The solution to this problem is not beyond a DIY fix, but it is a major undertaking. You would need to:
Remove all of the brownboard.
Inspect the ductwork and seams for gaps and leaks.
Seal the ductwork with mastic or HVAC foil tape
Air seal and insulate not only the ductwork but everything on the underside of
the floor. (probably with spray foam)
Then put it all back together.
I know it sounds like a lot of work. But at least you'll be at the beach:thumbup: