help - need solution to light roots & dark ends

I have no personal experience with gray, so I can tell you what I'd do if it were my hair...I always hope someone with more experience with gray will pipe up!

You can try going over your roots only - and even better trying to just do the parts that are lighter only - with a dark brown color that has a green base.  It will not come out green since you say your hair is reddish, red and green together make brown.  (If your roots are more orangy than actual red, use a brown color with a blue base).  Do the roots only or it will dull the reddish shade you wanted on the rest of your hair.

I'd still recommend test stranding just so you don't do your whole head if this isn't going to help.

Part of the problem may be that gray hair tends to have a thick cuticle and be very resistant to dye. Here are some tips for next time you dye your hair with the color you want to help avoid you having to go over the grays twice:
 Many people either switch to ammonia based dyes (because the alkaline Ph of the ammonia opens the tough cuticle), or try "softening" only the gray hair before dyeing - which means apply peroxide or developer only to the gray hair for 10 minutes, then dye it as usual.
A third method I've heard is to put only the color on the hair for 10 minutes, towel blot it off (old towel), then apply the color with the developer added.