Do a significant share of your sales happen on Amazon? If so, have you experimented with sending inventory into Amazon so they can do the fulfillment and you can get a Prime badge on your listings?
They do, but I've been reluctant to give more power to Amazon. They make us jump through so many hoops and come up with dubious reasons to deny payment, and handing over a bunch of our inventory to them gives them power to control us even more.