Despite not doing the normal "test charge" bit when I plugged it in yesterday, the car charged as normal last night, at full power for the whole charge.
If anything I'm more puzzled now than I was before. I've not had a scheduled charge fall back to 16 A for a fair time now, it seems almost as if, for me, the problem has just gone away. Given that others are still seeing this problem it's hard to know for sure what the cause might be. One slight difference between my charge point and some others may be that it delays switching on the control pilot PWM at the advertised current for 2 seconds after being plugged in. This was an attempt to emulate the delay seen by monitoring the car when plugged in to the Tesla UMC, during which the control pilot is at the digital comms pulse width.
I've had a similar experience, my scheduled charge has been happily achieving 32A for over a week now and I've not changed anything that may cause this. Let's just hope that's the end of it!