You might want to check out some of the B2B sites, such as Global Sources or Alibaba. There is a lot of fluff and filler, but I've had reasonable success finding companies for new components and processes from time-to-time. Once you have found a potential supplier, Google the exact name and see what comes up. Ask them for samples, or at least photos of current parts. My first foray into Asia was well before internet, but nowadays it's ridiculously easy. Most molders there will prefer to supply both the tool and the molded parts, and quantity/volume is not the issue it once was, as Chinese companies grow accustomed to doing business with the west. We routinely have specialty parts tooled and shot in as low as 500 to 1000 pcs. So you pay a few pennies more than if you buy a million. Make sure the potential supplier understands your estimated annual volume on the front end, and there's no problem. Some will invariably no-quote, but few mid-sized shops will turn away work.
My experience has been that a US company, offering the western face with Chinese tooling, as you put it, will run about 50% of the cost of domestic tooling. Sourcing direct from the molder in China, it is not unusual to see that figure drop to 10-15%. Just understand going into the deal that unless it is expressly agreed upon and in writing before money changes hands, it is understood that the tool will never be pulled or shipped to you. It's "your" tool in the sense that they will not run parts for other companies, but "your" tool may not run in another press without extensive modification. Ask them what the guaranteed tool life is, that is, the point before which there is no repair and maintenance charges.
For simple and utility parts, it's almost a no-brainer. High criticality parts require more homework and due diligence. I currently source about 100 components from 14 factories and trading companies for my current employer. I've had one single instance in the last 13 years where we had to change vendor due to unresolvable quality issues, resulting in a write-off of some parts and about $2500 in tooling, and have never made a single trip to any of the facilities out of necessity. It's no different than dealing with a local supplier, you find out whose word is good, and who is simply adept at making hollow promises to get the work. Many shops are adapting ISO methods, even if not yet certified, and they will be happy to tell you of their quality system and facilities.
It is better to have enough ideas for some of them to be wrong, than to be always right by having no ideas at all.