Just wanted to provide an update here, in case anyone else is in the same position. I contacted several private providers in NI, and only one was willing to prescribe Zyban for off-label usage for me (3fivetwo Group, Belfast). Their initial consultation appointment was £350, though. I have no idea what additional costs I may have encountered (e.g., how much the prescription would have cost out of pocket or if they would have required additional follow-up appointments).
Since I have a good relationship with my US doctor, I went to see her again when I was back home this summer. Paid $90 out of pocket for an uninsured consultation and then used a GoodRx coupon at Kroger to refill the prescription in full. I got over a year's supply of my prescription for $220.
Ultimately, since I was going back to the US anyway, getting the prescription filled there was a more economical solution for me. Given the situation, my doctor is willing to continue prescribing it as needed as long as I'm willing to come in for a consultation ahead of each 12-month refill. I plan to visit my family at least once a year, so I think this will have to be my long term solution until the UK gets on board with Wellbutrin for depression here.
Wish I had more success to report on the UK side of things....