Oh I must have used the wrong link then. Ok, the second untrained recording reads 145 Hz in my software, which is at the upper end of the male range, bordering on the gender neutral range. Your resonance and inflections are feminine already, so at that pitch you still sound feminine to my ears and undoubtedly do so for many others. So its a choice, really - I still would recommend to get a voice therapist to check your voice - see what your vocal range is, what your relaxed voice really would be like and if you can learn to use a little higher pitch without straining so much.
I think not using vocal fry would increase the perceived and analyzed pitch of your voice even in the relaxed mode, so just trying to get rid of that habit may make your relaxed voice go up in the gender neutral range and sound totally female.
A surgery might give you a voice that is pretty high - Dr Kims estimate for you would then be 220 Hz I guess, that is pretty average female speaking pitch and would be well above your trained voice in terms of pitch.
The differences between Haben and Kim are mostly in their technique. Both seem to be experienced surgerons, Dr Kim has I believe done over 400 vocal fold shortening surgeries now, Not sure how many Dr Haben has done, he seems to have used CTA for a long time and added vocal fold shortening later on? There are differences in their techniques - permanent sutures or dissolving sutures, laser or microscalpels, different points the sutures are put in,... but those are harder to find out because they do both not put up details of the procedures online.