Would you plan to stitch around the applique? Wouldn't that be tremendously costly if done by a long-armer?
I once quilted a beaded and embroidered quilt in a hoop. I think you would be able to get the hoop snug enough. As for those other issues, if you've hand quilted before you will know how to deal with the heaviness, and I think machine quilting would make the wool pop more than hand quilting would. I vote for hand quilting -- if you want to, that is.