Your medical will have been sent directly to INZ by the eMedical system. Medicals are scanned by a computer, and referred to the Medical Assessors if anything is marked as abnormal (or, we think, certain key words arise, though that isn't mentioned publicly anywhere). The MAs' job is to understand each applicant's state of health, and to do that, they have the right to require further tests and/or doctors' or specialists' reports, until they feel able to decide if this person has an Acceptable Standard of Health (ASH). Many people have been able to pre-empt the sort of requirement the MA will have by voluntarily going to their own doctor and asking for whatever it is that has shown up in their medical to be investigated, and for the doctor then to write up the findings, to be sent to INZ to catch up with their eMedical. (If doing this, you need to send it to INZ with full details of yourself, when you submitted your application, for what kind of visa, and add your eMedical number.)
The MAs deal with cases referred using a date-order queue system, as there is quite a wait. It is entirely possible to get the doctor's follow-up report to join your eMedical wherever it is waiting in the queue, so, with luck, by the time it is your file's turn for attention, the answers to the questions that might be asked are also there to be studied - and with luck, in your case, will explain the reaction which showed up so you can immediately be declared ASH.
No INZ timings, either mentioned on the INZ website or by an individual official, are EVER a promise. If you look around on this forum, you'll see people are enduring long queues at the moment for many kinds of visa. So don't trust the 11 months and 4 months you mentioned. However, in general, yes, a partner-sponsored work visa takes less time than a partner-sponsored residence visa to be processed. There is nothing against having two visa applications in at the same time - many people do this. As you have already applied for a partner-sponsored residence visa, the length of work visa you apply for will make no difference to what is needed for the medical - INZ
KNOW already that you want to stay long-term, so they will assume for the purposes of the work visa that you will be in NZ longer than 12 months, whatever time you put on the forms.