This might be possible with fresnel lenses for your monitors, Krusty.
I've never used them, but I believe that they come in typical screen sizes, though they aren't easily found for larger screens. The drawbacks I've heard about are that the fresnel lenses may hamper your resolution a bit, though, as they are usually made of plastic, and stand away from your actual screen a few inches. Also, I've heard that they tend to add some cylindrical distortion at the outer edges of the monitors.
That said, I've seen Youtube videos of guys who have used them on 3-monitor setups to create a seamless display for racing games.
Doable, but as the OP recommended, I'd suggest that you go for three screens. Even if the fresnel lenses don't work out, it's easier to get used to the bevels of the extra monitors being outside your focal point, rather than occluding it with the bevel area of two monitors. In addition, the cost of two fresnel lenses is similar to that of one decent-sized monitor, so a third monitor may be a better investment. Your call, of course.
FWIW,