@d-healey Thank you, Dave! I uploaded the 48kHz file by mistake, but as usual, your questions took me down the right paths to fix the problem.
To anyone arriving here having had the same issue:
When I opened the original sample file to check if it was the correct sample rate, I decided to re-export all the samples for good measure, and recreate the Samplemap from scratch. (Not a big deal; there were five samples in that map.) And now it seems fine. That was a critical issue for me — thanks again @d-healey.