Well - the pitch you have there is not relevant really. Usually they ask you to do a high, medium and low pitch sound to see how the vocal chords react in these registers. It has however not much to do with your speaking frequency, this is assessed by reading a text and recording it and then analyzing for the pitch.
Pitch alone is not all there is, it is just one piece in the puzzle. Undertones, Resonance , Prodosy are some of the others. I can only speak of limited experience now regarding the surgery, since I dont know how much is the Botox, the post op hoarseness and how much is the desired result of the surgery, but so far, the low and male sounding undertones are gone for me, lower voice limit is at 130 Hz and I dont have the undertones that would come from below that. Coughing and Sneezing and all that is still off limits for me if I can avoid it, so I am not sure how much change is to be expected there, but I think those sounds depend to a large degree on the resonance chamber? For singing , I guess resonance is important. I find it is pretty easy right now to use different resonances for me and I dont have a voice break really. Again, I am not sure which parts are because of the Botox, I expect some of the bad things to come back later on and I will have to deal with them somehow. From what I heard from the others, it is much easier to manage resonance and voice break compared to pre op though.
Dr Kim thinks that tremor can be treated with one or few Botox injections and medications. Apparently the thought is that the brain then unlearns these bad muscle use patterns (contracting the vocal muscles while using the voice) and adapts to the new, more balanced voice that can be used in a relaxed way, so no need to tense the muscles all the time. However if it is really a stronger variant of "spasmodic dysphonia" which basically is what the name of this condition really is, a more regular treatment has to be done. In severe cases this has to be continuously treated with Botox, but listen to the examples of people with this condition who get this sort of treatment and judge if this is you - I find this is a very different thing - they basically have gaps in their speech and sound totally damaged. I doungt that this is the case for you.
Dr Kim said if the post op examination (I will go to a local ENT and get an endoscopic video done again) and voice recording 2-4 months post op still shows signs of the tremor, he can give me adresses in Germany to get the Botox, but he apparently things that it will be enough to use the medication and then phase that out. But he seems to know doctors around the world who do Botox treatments.