Okay, I finished attaching the knitted border, and wound a few extra threads in for good measure. The blocking I did helped the border to lay flat, but the added weight of the knitted area made the piece sag when hung. What to do to counteract the effects of gravity? Fight gravity with foam! I traced the outline onto foam board, cut out the shape, and pinned around the outside edges, wrapping the knitted edges around the foam board. The entire piece is now flat, secure, and really easy to hang.
I don't think I will go any further with it, but I am now confident that I can use the addition of knitted areas in other works successfully. This was really a trial piece for the knitted border - for future pieces, I will choose much more interesting yarns (although I do like the subtle colour shift I got from this one).
Organic Study in Teal