The solution to preventing ice damming is to fix the cause. I mentioned in my 1st follow-up, FIRST, you need to be sure the attic/crawlspace is 'sealed off' from the main house. In winter, the warm roof melts snow and it freezes in your 'valley' due to a temperature change from warm to cold. If the cause of your ice is due to the 1) inability to drain water from the roof, or 2) the inaccessability of the valley to get water to gutters/downspouts, then you certainly need professional work. W/O seeing what's there (and I appreciate it's difficult to draw on the BBS), I've had to make assumptions.
I know your problem is between 2 & 3. Again, there's warm air up there that isn't being 'pushed out'. If you had soffits at 1 & 4, you would allow air in to push out the warm air through the gables. Thus, you've equalized air-in and air-out. It doesn't matter in your case where the valley is. Here's a few URLs to read to help you in a lot of ways, including answering your question about heating coils (to which I agree with them). Go to Ice Damming or More On Ice Damming or The Insulation Man (e-mail me). These articles will all tell you the same thing, again, irrespective of the roofing characteristics.
Sorry to repeat myself but maybe said 'another way', this is all I can add. My best to ya and hope this helps.