For anyone looking into this in the future, I've managed to do it via RunKeeper.
1) Add a RK goal with calories unit
2) Add a Garmin/RunKeeper automatic sync via the most excellent https://tapiriik.com
3) Garmin syncs everything to RK, and RK to Beeminder.
The end result is here
Note: RK will recognise all kinds of activities that you can have in a Garmin watch but I'm not how sure things outside of walk/run/cycle/swim will end up in Beeminder (Garmin allows you to categorise activities in various sports, like hiking, golf, etc)
cc @bee, @dreev