Agreed about the carpet dye being about the least expensive option short of ordering all new carpet.
Many years ago when I lived in Chicago, there was wax Factory I dealt with for many years called Nu Look. They catered and distributed largely to detailing businesses in the area, and beyond.
Made a lot of phenominal products, and carpet dye of basically any color you wanted could be had. Frank, the owner (been deceased many years) mixed up some pure black for me once, for my '68 SS396 Camaro, and while it was a stop-gap measure on the cheap, the carpet looked fantastic after, and the dye was quite durable, would not rub off.
I'm not sure how much luck you would have with an easily gotten product such as RIT Dye, but perhaps some here can point you in the right direction, or you may be able to find by search, specialty businesses on the web who specialize in making Dyes for vehicle carpet applications. I'm sure there's somebody out there who does.
You may never get an exact perfect match with such, but sure it would look much better than what it does now.
If it were me, I'd probably first try to "spot dye" the affected areas, and if the results were less than pleasing, I'd then probably resort to either doing the entire rear carpeting.
Hope I have not violated any forum rules, but here's a link to one such business who sells such dyes. You'll note they also make a bleach neutralizer that is used before dyeing.
http://www.detailking.com/store-home/auto-reconditioning-kits-supplies/carpet-dyes-and-kits/
