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 and some 3A. Modified CG.
Highly porous. Color over grey.
Best 1st day method: Super Soaker
Conditioners: Curl Junkie Beauticurls Strengthening Conditioner,
Deep condish: Curl Junkie Curl Rehab
Stylers: Experimenting with cones & sulfates while the dews are high. Sometimes try roller sets - classic glamor but I prefer my curls.
Every day is a gift