While FRC MAY cause eye-strain, most monitors on the market have FRC and it isn't generally a problem for most people. With that said, I try to avoid it too but it's hard to find monitors without it.
In your case, since you get eye-strain with two monitors but not one, it may be due to just the amount of light.
I'd suggest going smaller, using two 22" monitors for example at a decent distance instead of two 24" or bigger ones. Making sure that the new monitor has the same level of matte coating as your old one, making sure one isn't significantly brighter than the other, etc. Might have to experiment as well with VA vs IPS panels and see what works for you but fortunately, most 22" monitors are cheap.