OK, just a BoE Blue, which I still need to figure out what to do with, but it's an achievement, right?
And from there onwards, it was plain sailing:
And that answered the question "can you get the non-heroic achievement on heroic mode?" with a definitive "yes".
As we were on a roll, we went to peek our heads round the door of Utgarde Pinnacle on non-heroic, as it was the daily:
Oh, yeah. Easy.
So we tried it again on Heroic, sailed through the first two bosses – and then I can repeatedly turned into splinters on the gauntlet. Ah, well. No point in running before you can walk…