For the life of me, I don't know why I've been using such a huge inductor all this time.
I got a rev 2.6.1 board fab'd with an 0805 footprint for the inductor and tested it out, and it works just the same as the 2.6 version.
My inductor choice was a Taiyo Yuden LBR2012T100K 10 µH 360 mΩ inductor. As before, the boost converter had a 10 µF input cap and a 22 µF output cap. The rest of the circuit was the same (based on the ATTiny44A).
EDIT: Ah. Now I see. The LBC3225T100KR 1210 inductor I have been using has about half the resistance and a reel of them costs 25% less.