How do I edit my CMYK greens to output as brightly as possible?

 If you want bright, stay with solids.100% cyan +100% yellow creates a bright green.

If your definition of "bright" does not necessarily mean "saturated," you will have to tint those colors. Note that this is one of the things at which process colors (CMYK) are the least effective. 

Tinting them makes them not only less "dark" (the opposite of "bright") but also less "bright" (as in less saturated).

You don't have much choice to darken your color and keep it bright, you need to add more Cyan! Try C75 + Y100 and keep adding your cyan until you are satisfied. Forget about your RGB green, and work with the good old color system by adding your CMY values to keep your colors bright and mixing them as it's done with paint. Black will make them more dull so don't add any. Cyan + Yellow = Green Magenta + Cyan = Purple Magenta + Yellow = Bright Red Etc. And yes, your screen might not be perfectly calibrated, but even if it is, CMYK do look way "darker" than RGB colors. Trust your brain, if the Cyan + Yellow you choose to make your green looks like the best you can do, and if the suggestions for the Pantones are close, then these are the right (best) values.

Try C70 + Y100

or C60 + Y100