Well, you are definitely seeing first-hand the difficulties of a relationship between people in line vs staff officer billets.
In my opinion you have a choice of either biting the bullet now, or biting the bullet in the future. What I mean by that is you are going to have difficulty in aligning your billets, so you can either fix that now, or fix it at some point in the future and continue to be off cycle.
It appears that your significant other is a P3 person so the good news is there are plenty of jobs for them at any fleet concentration area for a first shore tour. Yes, JAX is the ultimate because that means you are an instructor and that is highly though of for future jobs/promotions; however, I know plenty who have taken jobs doing things like anti-submarine work in San Diego, or Joint Forces work in Germany, or work in Norfolk, or DC/Annapolis. So, with that he can really go anywhere for a shore tour, some will be better for his career though.
Now, the issue is that you will only be somewhere in the middle or end of PGY2 year when he is due to PCS (a lot of P3 NFO's get held on to for longer than 36 months ( I think the rule is up to 6 mos longer than original orders is allowable)) so what do you do then??? He PCS's and then by the time you are ready to PCS his shore tour is almost up (and those are almost never extended) and he is ready to PCS. (Although there may be some shore tour jobs for him in HI as well with the Wing or similar, but I haven't heard too many people excited about those jobs).
In my opinion, your best option is to do your intern year somewhere, say San Diego, and either continue on, or go do a GMO tour. Then when he is ready to PCS for a 2yr shore tour you will be very close to each others regular PCS rotation which then makes life easier for the detailers. You then have many options to follow him as a pediatrician or family physician to anywhere that plane is based out of and including his disassociated tour on a carrier or something similar.
I think if you try to go to HI for internship you may find it more difficult to get things lined up well, but again, it may be doable.
Also as to when to be married. Well the sooner the better in this regards. If you want to even have a remote chance at going to TAMC you must be married before the GME board meets in November. Sooner than that would be better in my opinion as it shows the program directors and GME people intent.
Anyway, all the best and good luck.