In some ways, Chase WoH card spending works against lifetime globalist, since it awards you WoH points which are useless except for point award stays, and those stays don't count towards LT globalist spending. But yes, as you say the only way to get LT globalist is $200k spent at Hyatt properties. Note that spending at on-site restaurants which are owned by the hotel will count even if you're not staying at the property, as long as you provide your WoH number when asking for the bill. Probably not a huge opportunity for most people, but some locations do have nice restaurants if you live near one.

For a while there was a partnership with Lindblad cruises which allowed you to earn base points on Lindblad expeditions. You could knock out a good chunk of LT globalist with an Antarctic expedition... unfortunately that partnership ended in 2023.