I do think the pieces added to the corners enhances the quilt, though not sure what you mean by quilting them first. I would just sew them together, then applique to the block first and quilt the whole thing later. Pity you hadn't thought of this before putting the embroideries on, would have been easier. I do a lot of unpicking, and would probably undo the block corners to sew them into the outer seam - but that's just me.
Your quilt is going to be beautiful. Hope I see it finished