I understand many here are reluctant to talk about this, so I thought I would step in with some professional counseling.  As this is becoming a common chronic irritant, more than a few doctors in San Francisco and WeHo now offer cock abrasion therapy.  It usually takes 5 weekly treatments involving gradually increasing exposure of your tonsils to a mild abrasive material, the result being the creation of a thin callous layer which will desensitize your oral cavity.  A mild topical anesthesia is used.  Your partner, or an on-staff TS, will test the results at the end of the program .... at no additional charge.  Unfortunately it does not cure the hoarse voice you mentioned.  Many of these doctors also offer gag suppression therapy which involves both physical and psychological methods.  Some insurers will cover these; the medical code on the doctor's billing must be indicated as (O).
Hope this helps,
Dr. Phil

Yes, it happens all the time for me after a good skull fucking.  Sometimes it's barely noticeable, while other times I can be a bit sore for a few days.  I agree that with you on "her doing her job" except I'd bump your 1/2 second of panic up to a good 15 seconds.  I would suggest you do the same and you'll have a much better time.  I'd also suggest not eating for at least a few hours before.  That way you avoid the chance of ever puking but still get an amazing gagging experience.