Ok, couldn't leave it be. I went back to my original assumption that they had placed a RY3820E on there in the first place, instead of RY3820. RY3820 is 600kHz, RY3820E is 500kHz - and that would explain why the BMS had the same behavior when I replaced the chip with an RY3820E. So I put in the STI3470 which I knew was close to the RY3820, 600kHz and all (and because the original RY3820 is pretty impossible to get). Result: no more noise in the BMS nor the charge controller. Output voltages of the converters all fine as well.
I'll run more tests later. Sleep first...