I have pretty much the same problem. I find it very difficult to get a rich brown that doesn't have ugly orange tones.

What I compromise with is using a neutral brown (like light brown or dark brown - not ash) and mixing some golden blonde with some of the light brown and streaking that in. This is how I do it.

As the roots come in: I make one bottle plain light or dark brown (depends on how light or dark my hair is currently). Then I make one bottle mixing the light brown with medium golden blonde. Then I will alternate applying it to the roots - usually two "streaks" brown with one streak mixed. By streak I mean when you part your hair with a comb and apply the mixture to the roots.

The result is subtle warm highlights throughout. Someone who cut my hair thought it had been done professionally - she complimented the color job.

I use L'Oreal Preference. Henna doesn't cover my gray so I stick with the Pref.

HTH. Let us know
ETA: I just re-read your post and you want reddish auburn highlights, so this might work with an auburn bottle instead of the blonde. I look hideous with any red so I use the blonde. Good luck!!!
2/c Coarse hair med. density.
Highly porous. Color over grey.
I love all the Curl Junkie products. Still experimenting with gels and curl creams. Still hoping for 2nd day hair....
Every day is a gift