...it was sometimes good, sometimes a struggle (I changed companies twice over a short span, and insurance companies 4 times in that time).

Some HD plans have a list of covered medications (don't remember the exact term, but that's the idea). With one of the plans we were on, my daughter's insulin was completely covered right from the start. There was a big list of covered medications.

The other thing to consider is the actual math involved, of when you hit your deductible, and then when you hit your out-of-pocket max (if at all). Because my daughter's medications were so expensive, and due to a few hospital visits, we hit the deductible pretty quickly. At that point, "expensive" medications were mostly covered the rest of the year. When we did the math with the lower monthly premiums, we were better off with the HD plan. And, the hindsight proved that out.

Since the OP is asking about HD plans vs traditional plans for his church employment (I think I read that right?) that traditional plan would be DMBA. A lot of people LOVE DMBA, but to your point, the people who do not love it are those who have expensive medications. I don't know the details, so the OP needs to research this, but this same daughter also was recently a church employee with DMBA coverage. Her comment to me as I was helping her navigate a DMBA claim denial (she had my insurance as secondary) was that DMBA was great for healthy people, but not good for people with chronic health issues.