You could also get a second rear wheel and put a 11-36 or 11-40 cassette and combine that with a smaller chain ring. That’s less of a hassle and cheaper than a second bike. Personally, I’d err on the side of having an easier climbing gear.
In any case, I don’t think climbing and 1x is mutually exclusive this day and age. My new road bike is 1x12, and we have long, steep climbs where I live. (The longest is about 1,000 m of elevation in one go, but we have multiple other shorter ones of about 25-30 minutes.) My smallest gear is 42:36 = 1.17 and the longer climbs are very much doable. And I spin out at 60–65 km/h in my 42:10 = 4.2 = 46:11 = 50:12.