Dunster,
I don't see the background as drab, more subtle! :D
Here's what i would try - you have a very purple hex top left - put it in the middle, then all the other purple ones around it then radiating out into the drabber, sorry, SUBTLER blocks! Then maybe an inner border (maybe one of those skinny ones she talks about in the book) then an outer border with your oriental appliqué idea, again picking up on the purple; BTW I think I've got some of that fabric - a left over from my Mum's neighbour, but only a fat or so! :D