If you have not tried Rit Dye on your reed for basket weaving, give it a try.
I have found that it works really well.
I use the liquid Rit Dye and put 2 cap fulls into about 2 gals of water, the colors come out extremely well. Add a cup of salt and water softener if you have hard water, bring it to a boil and then add your reed, let it simmer for 1/2 hour or til you reach the desired color. Rinse really well after you take it from the dye pot. Let it sit over night and then rinse it again really well before weaving with it, let it dry a second time and then weave.
You will have to be careful of bleeding. It seems that all the commercial dyes will produce bleeding, but with some care and use of limited wetting while weaving you can reduce this danger.