A company would probably not give you the time of day, but there are hordes of garage hackers with the equipment and knowhow that you could hire on a consulting basis and get some PCBs made and stuffed with parts.
$10,000 sounds like a nice tidy price if you're trying to get a small quantity of boards built and shipped.
You didn't mention how much you have designed so far. Is this just an idea, or are you all the way to a schematic with bill of materials? The closer you are to the latter the cheaper it gets. And if you DO have a gerber/BOM, there are turnkey services that can build the boards for you outright, like PCBWay.
