Here's an update on how this ice bottles in water bath method has been going for me:
The stick on thermometer no longer works, so no idea what actual temps have been (can be sure temp never went above 21C).
OG was 1.032 (lower than expected, but that's a separate issue). In under 5 days it was down to 1.013. After that I have been far less vigilant about replacing ice - doing it maybe twice a day (morning and evening). Another week later and it's now down to 1.009.
I tasted the sample and it tastes amazing.
Over the next 48 hours I'm going to try to crash chill (using 2 x 5kg bags of ice from a petrol station, each 24 hours I'll pour one bag of ice into the 60L plastic bin that my FV is sitting in), then bottle and leave in normal household fridge for as long as I can hold out).
I won't be bothering with this method again. I'll be hoping to acquire for a fridge or freezer before I attempt a proper lager again.
I will, however, try to make this same beer again using the same yeast and just leave at my ambient wardrobe temp of 20C. But then again, maybe chilling while the ferment is generating it's own heat is a good thing? Wild temp swings didn't seem to adversely affect this current batch. I actually want to drink it all right now - directly from the fermenter - it's that tasty.