Would some other kind of insulation a)be possible and b)improve the
situation for the future of this room? Heating wise, we use/heat this
room for approximately 12 hours a day and close it off after dinner with
lovely plastic accordion doors and close the heat vent.

Any kind of insulation is possible but the insulation is only a part
of the problem. the bigger part of the problem is ventilation. If
you atttic were properly insulated AND ventilated then ice dams would
be minimized. The insulation should not be touching the bottom of the
roof. there should be an air gap between the insulation and the roof
ideally.

Would the heating cables along the edge of the roof be a good solution
for this small expanse, maybe 14 feet? There is an outdoor light, which
I despise, mounted at a corner and would happily see it turned into an
outlet for wires with a switch just inside on the wall.

Heating cables are a good solution. They just cost you to operate
year after year.

Read in the paper today about a metal roof snow slide? Anyone have a
ballpark on what that might cost for this small area, and does it seem a
reasonable idea in this situation?

Not sure what you mean but metal roofs often have a diverter which
directs water away from say an entry way. Although I have seen them
used with metal roofs I'm not sure it would be compatible with other
materials.

For the immediate moment, meaning tomorrow being the one day
accountant/it's-tax-season mister will be home, we want to make some
serious headway with the ice dam itself. I read about making the
pantyhose filled with melt chemicals, and wonder can we just spread the
chemicals out all along the ice dam and clear the whole thing off over
the course of the afternoon, instead of just creating the drainage
channels? The height is very low, so we'd be able to reach it all from
the edge with the stepladder. Is there any reason not to spread the melt
stuff around on the dam?

That is what I do. Just climb up there with a bag of salt and
sprinkle directly on the ice. After it has had time to take effect
you can go back up and gently push the ice off the edge with a plastic
shovel.

What I do is, after a large storm I just go up and shovel the entire
roof. it's a bit of work but totally solves the problem. ice dams
can cause a lot of damage to your house when they melt so please do
take care of it right away.