I've received a lot of responses from alibaba for only the chips. Such a waste of my email.

I should note that the price for RT5350 to be around $1.5 .

The cheapest module costs $6 per piece for 1000 units.

I think manufacturing a board with a BGA chip would probably cost a lot of money.

Some sellers responded with offering assembly and PCB manufacturing, so I'll decided to send over PCB files for the VoCore which uses RT5350 and is kind of the module I would want to buy, but it's expensive (20$)

VoCore has all the board files on their site (link) so I'll just send them over.

I contacted 4 sellers for the PCB and manufacturing

I also contacted sellers for the HLK-RM04 module.

Price for 100 pieces: $7.8
Price for 1000 pieces: $6.5

This seem to be the best prices for this module.

I also received a response for a different module (TOP-AP01), at $6

Link to module.

I'm also starting two new inquires. One for the linux board (like VoCore and the modules above) and one for USB linux camera.

I also found a list of similar modules on the openWRT forum (link)

I'm sceptical about finding a cheap, HD webcam, but it may be possible.
The one used on the VoCore blog (link to blog) cost $9.71 on Taobao (link to product).

Today I spent 1.5 hours on this project.