Going back to the oscilloscope, like Mark says I'd be looking at the signals going into the BT module and making sure the minimum highs and maximum lows are good, looking for noise, glitches, overshoots etc. Bit hard to say until you see it as you don't really know what the problem is yet. But certainly would give some kind of indication of which side of the dividers are having problems. Depending on that you may consider proper buffers. Even some minor filtering *might* be enough for those sorts of issues.

The BT module inputs should be pretty high impedance but that might be where the dividers are coming unstuck using fairly high resistance levels.

I2S is a higher frequency than I was thinking. Of the order of 10MHz+. That might also be a bit of an issue with the dividers and the capacitance in the resistors. Proper level shifters would fix that.

Put it on a 'scope with a >20MHz bandwith (preferably more in case the clock frequency is higher than 10MHz)