You might want to consider a hot knife for this kind of work. Micromark makes this one...
Hot Knife Link
I think you may be asking a lot from the WS hot wire cutter. IOW, their device was basically selected as a tool for the construction/contouring of their white styrofoam products. If you go to their website, look through their how-to videos, you'll see that cutting 2" open cell (Pink/blut) foam is not one of their demos. Most of their use of their hot wire is on relatively thin (~1/2") closed cell foam board.
Another thing I've found is that the thicker the foam piece, the slower you'll be able to move the wire through. The wire must stay hot to 'cut'. But in cutting the foam, it's also losing heat locally to the foam. If you move too fast through thicker material, the wire will not stay hot enough to cleanly cut. Too much pressure/pull, and the wire will fracture.....I'm sure you've experienced that from your request.
Also, depending on how big a power supply they've provided (the wall wart, so to speak) the heating rate may not keep up with your cutting motion. Bigger diameter wire, as you've requested, might exacerbate the problem....requiring more power. Besides, if you are drawing the wire through 2" foam on an angle, you're cutting a LOT of foam with that wire based on the harp size. A 45-degree cut through 2" foam is actually nearly 3.5" of cut width....a long way from WS's demo usage.
Then, too, be it a hot wire or a hot knife, you really need good ventilation when doing the cutting. The fumes are not what your lungs need to experience for long periods...even short ones!
That said, I'm doing a lot of cutting of the pink foam myself. I have acquired a couple long sturdy knives of the kitchen variety that work well for this job. One of them is serrated....like a bread knife. I also have an electric knife acquired from a garage sale....you know, the two oscillating blades that were once all the rage for carving the bird on Thanksgiving??? It works well, too. I keep the blades clean and sharp (believe it or not, cutting open cell foam dulls blades after a while.), and occasionally apply a 'lubricant' to them....like a coat of wax or dry silicone spray. Sure, they'll make a little static-y foam dust in the process, but a small shop vac kept handy takes quick care of that. No fumes, though.....you know, happy wife, happy life?
Just some thoughts, FWIW...