Well, I never heard of shutdown processes, but now I have I went out and redid the check, exactly as above, an hour or so ago, when I got the 0.22 readout, and...
Much lower. Also, arguably interestingly, all over the place. Fluctuating constantly, between about 0.06 and 0.12. I'm curious about the variation - I would have thought if there was a drain it would be consistent. Apparently not. But assuming it averages out at about 0.09, that's around twice what I've heard is 'to be expected'/acceptable. And would probably account for the battery losing its grunt over a few days.
I'm thinking, as a quick & dirty solution, fit the solar panel, hard-wiring it to the battery terminals so it's isolated from the
battery isolator, as per Gwylan's tip up-thread, then simply add 'bip battery' to the regular startup routine. Sounds a belter, eh?