I would just do a full head of Highlights and take it through.
However it's a conversation you need to have with you hairdresser. Explain that you don't like the warm tones still in the hair, and feel it's too dark through the mid lenghts.
If you don't think your hairdresser is listening or giving you what you want then tell them or find a new hairdresser, but unfortunately it's hard to advise without being able to touch see and feel your hair x