Sorry, don't have any useful feedback to offer you, but we have had a few people on here previously, asking about medical waivers, so there's hope that someone will tell us how they got on and how the procedure works.
This is what the INZ Operations Manual says:
A4.60 Applicants who will not be granted a waiver (13/12/2001)
See A4 Effective 28/11/2005
See A4.60 Effective 26/07/1999
Applicants will not be granted a medical waiver if:
they require dialysis treatment, or a consultant physician has indicated that they will require such treatment in the immediate future; or
they have active tuberculosis (see A4.60.1 below); or
they have a mental disorder or intellectual disability that has needed care in a hospital or supervised residence for more than 90 days in the last 2 years; or
they have a physical incapacity that requires full-time care.
A4.60.1 Applicants who have tuberculosis
Applications from people who have active tuberculosis must be deferred until at least 6 months from the date anti-TB treatment has begun, and applications will only then be approved if:
sputum and/or gastric juice is negative on culture for tuberculosis; and
the applicant continues to meet all other policy requirements.
so it looks like you could be in with a chance if INZ can only get their heads round the costs.
I don't know if you've read this previous post about
medical waivers . You might get some idea of timelines from it. Although Taormina doesn't appear to have come back on that particular thread and I don't know if she's followed up on another one, she is still looking in on the forum so maybe she'll be able to help. Otherwise perhaps you could send her a PM.