I had the same problem. I purchased an LED strip from ebay. This strip is 16 ft. long and is 12 volt. You can cut the strip in lengths of 3 lights and either solder leads to the strip or purchase connectors from the same supplier. I removed the ballast and bulbs from the fixture and replaced them with 4 strips cut to length to fit. I had enought LEDs to modify 3 fixtures for less than $20.00 and my problem was solved. PM me if you need more info.
Several years ago I dyed the carpet in my motorhome. I used Rit dye mixed up in a spray bottle. I used a fairly weak solution and scrubed in in with a scrub brush. I worked really well and had very little crocking. You might try in a section of carpet not visible such as under the bed or sofa. If it doesn't work for you and you recarpet anyway, what have you lost.