I cant recommend any suppliers as you don't have enough detail about what you are going to mold. However, in my experience china can be quicker than that by often not by much as cot is the big benefit by going offshore (1/2 price tooling).
With those lead times you also have zero margin for error, weather its finish related, dimensional, or expectations of a new to you supplier. Having to rectify any of these issues with a molder will be devastating to the timelines that you have mentioned. Unless you fly to china it is also likely to take longer to resolve any of these issues.
If your deadline for production is hard and fast, you might want to look into getting some parts started as a buffer with a quick turn prototype service like protomould.