And we're alive!
That was quite straightforward, I found a MicroPython library for the BME280 (https://github.com/robert-hh/BME280) and updated my sensor code (https://github.com/VirtualWolf/esp32-sensor-reader-mqtt) so it can use either the DHT22 or the BME280. And as a fun additional point, the BME280 library also calculates the dew point based on the current temperature and relative humidity!
I don't have it running "in production" yet, I've just got it hooked up to a spare ESP32 and it's sending its data to an MQTT broker running on our Mac mini so I can keep an eye on it for a while, but it's very interesting comparing the values between the two sensors... right now the DHT22 says it's 20.2˚C and 94% humidity outside, the BME280 says 19.9˚C but only 71% humidity. I also want to get a better enclosure for the whole setup as well, I'll think I'll ask a friend who has a 3D printer to print me out one of the multitude of Stevenson screens that seem to be out there.