Hey @Nic Hubbard,
I spent most of the afternoon today out caching and made about 25 logs with Cachly. All logs look good date wise, so I'm pretty happy with that. I only had to refer back to "the other app" on a couple of occasions where I had corrected coordinates stored, but hadn't migrated them to Cachly (or geocaching.com) yet.
So I'm pretty happy with the way this app is now working with regards to the dates. It all looks correct (although I'll probably need to test one day around the midnight cutover, but that won't be for a while yet).
Thanks again for all your work on this issue!