You're in luck, because the Radeon R9 200 series is compatible with crt_emudriver. It has a DVI-I port, yes? (possibly marked VGA, or with the square wave icon?)
Before you start, make sure you have your windows key and that you backup everything you need to, perhaps even making an image of your windows partition, because wanting to use a modern display along with crt_emudriver and an old analogue one can get you into trouble. It's really hard to go that far wrong, but not impossible.
Next, go here, and make sure to pick the correct download! http://geedorah.com/eiusdemmodi/forum/viewtopic.php?id=295here
Then uninstall your current video driver, and as a test, follow the guide in the next link, but only up to the point of emulating the EDID for the DVI-I port. You do not need to either generate or install any modelines, IIRC. That comes later. If you've done this part right, windows display properties will show a display connected to the DVI-I port called Generic_15, or Arcade_15, or whatever preset you picked. (Generic_15 is safe for a TV). There's no actual display plugged in there, obviously, but getting windows to think there is is the first step.http://geedorah.com/eiusdemmodi/forum/viewtopic.php?id=301
If this seems ok, start playing around with your modern displays and make sure everything works as expected. Can you load AAA titles still? the version of crt_emudriver you'd be using is Crimson-based, so you might be ok. If you're happy, you can then go and drop some money on a VGA-to-Component transcoder, making sure it can handle 15kHz (low res) modes like (640x)480i and (320x)240p. You then get a DVI-toVGA adapter for $2, and a VGA cable.
I don't know much about those transcoders, save that a decent one is north of $100 if not by much, introduces no lag, and has very, very little loss of video quality.