Find an engineer that can't get what they need.
Yep (engineer here). Get an engineer at a company that's not missing dollars to save pennies and solve their problem.
If you want R&D or first run sort of volumes then the only way to get the purchasing guy's attention is to throw something well out of the norm, and then be able to back it up. The only supplier I can think of off hand who might be able to get away with this is a swiss shop I used a few jobs ago. They were so competitive on precision round stuff in 10-500k/year volumes that they were sending parts to China for a decent (10-20%?) portion of their business, and they hadn't made a reject part in years (yes, really, and we were checking). Not one late shipment, dinged part, missed finish or tolerance, nothing. Few can pull that off, I know I can't.
Now, when I have a problem on 1 to 100 parts, I'll ask the shop for a quote, then tell the purchasing guy "Send this order to this place for this amount". Some places are cheaper than others.
The hard part is finding that one odd problem, then not missing any of the reasons that we're still using the problem shop. One place for example had a hard time making things the right thickness (4 tenths on thickness). Not all that hard, half the shop could do it in their sleep. Unfortunately we often got the other half of the shop. Thing is, they'd fix it fast, they had a TON of spare capacity so we could hand them a huge pile of stuff out of nowhere and they wouldn't quote us a 10 week lead, and reasonable sized orders came back under 3 weeks. My manager also didn't understand that they weren't really 10% cheaper compared to local options because of the time spent getting them to fix things, so I had a really hard time getting anyone else in the door, and I'm sure the shops that I spoke with felt it was difficult as well.
If you don't want to touch anything under 100k parts/year (I suspect that is not the case here) or at least a very consistent job then you probably need the buyer (or purchasing agent). As an engineer by the time I'm having a problem on 100k parts/year there is almost always an obvious and effective solution, but it costs $0.01 more per part and if that cost gets approved by someone above me it will do so at the current supplier, or at another supplier willing to eat in to their margin that much more (I don't ever want to be a high volume automotive supplier).