I grow three different "gingers" - white (Hedychium coronarium), kahili (Hedychium gardnerianum), and blue (Dichorisandra thyrsiflora) (though that one has yet to flower so I can't say for sure that it's what it claims to be, and it's "not really a ginger" anyway.)
You may be under-watering - it's somewhat hard to diagnose over the internet, but both looking crispy and your comment of trying not to get the soil too moist lean that way. I water mine until water comes out the bottom of the pot, and if it's hot I'll leave some in the saucer. My original white ginger (much expanded from a "soil-free inspected plant in a baggie at the airport in Hawaii", and split quite a few times) is now 25 years old, and has never had issues with root-rot or the like. I'd probably plunge yours in a bucket for 20 minutes, then pull it out, drain for a minute or two, and return it to a saucer. I'd say both of those look a little crispy, actually - just one is worse than the other.
Each stalk does also just die back as they age, and new shoots come up, but I don't see much in the way of new shoots on your plants. As an additional thing that's difficult to tell over the internet, I'm not much liking what I see of your potting soil; seems very bark-y. You may just need to await new shoots - see if there are any green/red spots on the rhizhomes thinking about putting up new shoots.