That's great that you are feeling ready for surgery. Yes, you probably can't avoid a mastectomy based on the current standard of care, but if you do TCHP you have a 50/50 chance of it working.
I did want to correct your statement about chemo being the older standard of care, just in case anyone else reads this and gets confused. It is unlikely that with early stage disease and a hell of a lot of patient pushiness that any tumor tissue will be tested for mutations beyond what is normally offered to any breast cancer patient today.
From my stage 4 sisters I have learned about live tissue testing through organizations such as the Weisenthal Cancer group -- where they take live tumor and test to see what chemo it responds to best:
http://weisenthalcancer.com
Foundation One testing is another common one, done to sequence preserved tumor tissue in order to test for certain mutations that are common to cancer.
http://foundationone.com/
Other labs do different tests as well including tumor antigen testing, a cornerstone of the developing immunotherapy field:
https://en.m.wikipedia.org/wiki/Tumor_antigen
Unless you are very wealthy or influential, I highly doubt you are being offered better than standard of care. The only difference being that you lose out on the opportunity to know that neoadjuvant treatment was effective.