Small bit of progress. After the solder rework station turned up I set about desoldering the regulator and one of the Schottky diodes (MUCH easier this time around). However this has still not reduced the power consumption below 0.15mA. I have one more idea to try before just accepting the 40 day or so battery life.
I am now however happy to run everything off the battery, so the project is at least mobile now (albeit still on a breadboard).
I've also spent a bit more time on the software. The ability to log fresh insulin (and hence clear the min/max temperatures) is in, along with a battery gauge page (although I'd like to add a small battery indicator to the default page too).
I'll post pictures or a video when I can. Git repository has been updated.