I am a developer of a cheap product and i have no experience in mass production. Device is fully functional and represents a single sided PCB, a microcontroller, a bunch of diodes and a few passive elements. However, MC is kinda overkill and schematic could be done with some simple TTL/CMOS logic and passive elements. I can easily create VHDL or logic equivalent. I can't use standard logic IC's due to size restrictions. It would be best to use a few hundreds of transistors on a custom chip, if that's possible. I saw a ton of devices that are ridiculously cheap and have some circuitry in COB. This one costs 10c shipped, that's 4 times cheaper than a MC in my PCB I had no luck finding a suitable manufacturer. I found some MPWs like MOSIS, but that's obviously not what i need. So, is there a way to create about 10k of devices with cheap custom COB?
A custom chip for 10k units is unlikely to be cheap, as the masks will almost certainly cost more than $1k, which means your chip cannot possibly be made for $0.10. The reason the one you've found costs $0.10 is because they sell in a much greater volume (100k-millions), so the cost of masks and setup for a production run is spread over many more units.
That being said, a chip like the Silego GreenPAK might be a good option for you, as it's a small and extremely cheap (the cheapest on mouser is SLG7NT4375 at $0.195 each for 1k) CPLD. Assuming your design fits and doesn't need too much analog functionality, this should work for your use case.
A micro controller isn't necessarily overkill, and may also be pretty cheap. For instance, the lowest cost mcu on digikey is the ATTINY5-MAHR at $0.14 each for 1k. Additionally, if you're willing to navigate the markets in asia, prices can potentially be even lower.