I am no longer red head, but I have had every shade of red hair in the past. The most important thing about shampoo is NOT to shampoo everyday. As long as it's a gentle one, it really doesn't matter what brand it is. Personally I like Aveda sap moss, shampure, TiGi bed head dumb blonde and Aquage color protecting shampoos. Condition well.
I'm surprised you're not using any color deposit shampoo or conditioner. I really prefer color deposit CONDITIONER because they deposit colors much better than color deposit shampoo. Stay away from ARTec color shampoo and moisturizer. While their color selection is huge, most red shades are too pink, and texture is too drying. Aveda makes good ones -Annatto, bixa and madder root. Or even better is their Personal blends conditioner. At Aveda stores, you can pick 2 colors and a scent to get a conditioner just right for you. You can also get matching shampoo. I would recommend using these 2-3 times a week Graham Webb color deposit shampoo and conditioner are also good, but these have been discontinued. If you can find it, Goldwell color glow treatment is great. I used to love stay red treatment.
That orange brassy tint can be fixed by using blue lavendar color deposit product once a week. Aveda blue malva is a good one, and A/G sterling silver and Clariol shimmerlights are also great.