My shop is set up in imperial units, but I want customers to order in metric & receive confirmations in metric units (or vice versa)

It you want you customers to have an order confirmation in their units, you'd have to set up another output page called "Order Confirmation Metric". This output page needs to be a Parts List style output page and also have the setting to "Show Parts on this Output Page" checked. 

 Then go into your products and create a metric conversion part. Here you want to use any formula you want to show on your metric output page, and duplicate the formula then multiple or divide by the conversation you want to achieve, then set that to show just on the one output page.