Thanks for the suggestion. I tried that, and while it did allow the waves to start at non-zero times, for some reason it through off the quantisation, and the loops sometimes started out of sync.
But - I think I’ve solved it another way. I turned off stream caching (I must have turned it on at some point while experimenting) and also increased the max cache size. For some reason, that stopped the streaming waves from playing at all, but when I switched off force streaming and seeking, it works. For now, they seem to start properly quantised and on non-zero start times.