1950's ranch-on-a-slab in western NY. This is our first winter in the house.

There are ice dams front and back. We've been reading up, know about
improving overall ventilation, etc. The most immediate situation is on
our 3-sided room that sticks off the back of the house (faces west-ish).
It's more of a porch-like 3 season room, made 4 season with the addition
of a heating duct in the wall adjoining the original structure of the
house. The roof/ceiling is not very thick on this room. The ceiling is a
drop/acoustical tile ceiling, and when you push up the tiles, there
are only a couple of inches before you touch the insulation, which I am
assuming is up against the underside of the roof? It appears to be foil
backed bat insulation (?). From where you enter the roof off the
kitchen, the ceiling slopes from the standard 8 ft down to about 5.5ft
at the furthest wall.

Today was sunny and temps were up a bit, and I noticed seepage above and
around the windows in this outermost wall. No gutters, no eave on this
extension, and a very thick ice dam at the edge, probably 4-5 inches and
extending up the roof a good 3ft or so. There were some impressive
icicles hanging, which I chipped away quite handily with a rubber mallet
and a cardboard box to protect the windows. Lots of runoff while I was
out there.

I did a bit of this chipping along one edge of the roof surface from a
ladder, cleared maybe a couple square feet, but got tired fast (I had
roof-raked already) and worried about all that pounding on the thin roof
of this room. The overall roof is in good condition, we're 6 years in
on a 30yr asphalt roof.

Questions:

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.

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.

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?

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?

Any other suggestions, besides the very helpful ideas of moving or
demolishing the room, would be appreciated.

Karen