"So my question is who do i call about addressing this situation, an insulation company or a duct expert? "

Duct expert,I can't say which one 777,but certainly NOT the one you had out to start with unless it's partly under warranty. I'm going out on a limb to say that duct would have to be without insulation,not simply poorly insulated to cause this. Long story short,warm air from indoors is spilling into attic. From attic it flows out soffit vent where it condenses and freezes. Most likly several small air leaks or a single duct totaly disconnected. The professional way is useing smoke test but a smart guy willing to skamper around the attic can be pretty effective in finding and repairing loose ducts.

I am trying to follow what you described. For 4 years you had a damper closed and had poor air flow to upper floor. You open the damper and now the second floor can cool down in the summer. Obviously this damper should have never been closed in the first place.

Now it is winter so I would think you want this damper to remain open. When it was open did notice the upstairs was warming up faster than it did previously?

Believe it or not, the icicles forming on your roof is a good thing. This means your attic is staying cold and little heat is escaping. Take a look at your neighbor's houses. The ones that no snow or ice on their roofs have a problem with heat escaping, the ones that are covered with ice and snow are well insulated.

What may be happening is when you close the damper, the duct work behind it leaking and the warm air is escaping and rising into the attic. This is keeping the roof line warmer and melting the icicles. My suggestion would be to keep the damper open and enjoy the heat inside the house. Visually inspect any exposed duct work for leaks between seams. You can seal these yourself or hire someone to do it.