I am considering leaving my current employer. Hypothetically, assume my new employer has a different health insurance provider (although, it probably doesn't matter, since it would be a different group policy).

My current plan is a high-deductible plan with an HSA that my current employer funds with half of the year's deductible. My plan also has an annual out-of-pocket max per person in my family and for the whole plan. We have already had a few appointments that have ticked away at that annual max, but I fully expect to blow past it (on my wife's oop max, at least) when my wife gives birth to our second daughter in June. Thus, a large portion of the hospital stay for my wife and subsequent trips to the hospital will effectively be free for her after she goes into labor, due to hitting her annual limit. She had a major issue post-delivery with our first related to her spinal, so, while not expecting a repeat, there is precedent for follow-up hospitalization.

So, my concern is this:
If I change providers, my understanding is that limit would reset at the new insurance provider. Do I have any options to mitigate this?