i think the ribbon idea would work if that's the way you choose to go.
i had to struggle with this for a while because i reeeeeelly don't want to sound critical or discouraging. if i were to be totally honest, i'd have to recommend you remove the minky instead of adding to the other blocks. i think you'd end up with a more sophisticated, feminine top.
if the [currently] framed blocks are still larger without the minky, you can trim them back to match with no damage to the look of the piecework.
once the blocks are matched to size, you can put sashing between them to achieve the "frame" you hoped to get from the minky. you could use traditional frabric ... OR ... you could use ribbon if you want something very different. a medium weight ribbon, at least one inch wide (i'd recommend at least 2") would do nicely. if you're worried about wear and tear, you could reinforce the sashing by adding the innerfacing (or muslin, or any other lightweight but reliable fabric) to the back after it's sashed, and topstitching to hold it in place.
clear as mud?