Hey I did a very similar setup.
Mine was eyefinity with 2x 1600x1200 and 1x 1920x1200.
So what you should figure out is what resolutions does each monitor support?
For example, I'd guess that your 1920x1200 will also support some 16:9 resolutions, very likely 1920x1080, but also maybe 1600x900.
Then, will your 1600x1200 also support 1600x900? If so, you are golden because then you can have undistorted triple screen. Now granted, your 1600x1200 monitor will be letterboxing with black bars on the top and bottom, but that is very minor and you are probably already used to letterboxing on your 1920x1200 when you watch movies etc.
Anyway, eyefinity will look for a common resolution for all three monitors, and use that for all three at the same time. Hopefully you can find a resolution like 1600x900 where the picture will not be stretched or squeezed on any monitors. But think if you had to use 1600x1200 on the 1920x1200 display - that display would stretch it out and distort it, so not ideal.
Let's assume the worst and say you are stuck with a very poor choice of resolutions on the 1600x1200 display, e.g., it refuses to be run at any 16:9 or 16:10 resolutions. You still have two ways to solving this to avoid distortion:
1) play a game that lets you adjust the pixel size. One example would be Chronicles of Riddick. There is a menu option that would let you adjust the aspect ratio in the game and that would let you "undistort" a stretched screen. Maybe other games are like that too, I'm not sure.
2) add a desired resolution to the ones your 1600x1200 monitor will support. You do this by editing the EDID info. It's a rather easy process, you first obtain the info from the monitor using a first utility, then you edit it using a second utility (to add the desired resolution), and then you save it as a driver and install that and voila your monitor will support the new resolution.
Anyway, I say go for it, but keep in mind that you may be constrained by your "cheapest" monitor if it doesn't provide options for supported resolutions.