What sort of volume? And if you're looking at current shunts, I guess the surface doesn't need to be bare copper, but can be plated?
You could get whatever size and shape you want laser cut or stamped out of sheet metal. Stamping can be very cheap if you've got enough volume to amortize the tooling/setup cost, and any company that does electronic stamping should be able to acquire pre-plated sheet coil, so they'd be ready for soldering after stamping and cleaning. For assembly, you could probably get some custom plastic trays CNC milled, or maybe stacked out of laser cut sheets, to standard JEDEC sizes to go into a tray feeder. Loading the trays from the bulk stamped parts might not even be too bad, if the wells are sized correctly you should be able to just throw a handful of parts onto them and shake until they settle into place. Some assemblers may even be able to place loose parts out of tray wells, for example Europlacer machines have that as an option.