4: custom ASIC..? Isn't this like... reallyyyy expensive?
It all depends on quantity - tooling/design cost is expensive but unit cost can be very cheap, so if your volume is high enough, the savings on unit cost pay for the tooling. Your functionality is simple enough that design & tooling costs are probably relatively low (at a not-very-informed guess, probably 4 figures).
5: Let say 80 unique object, 20K units each?
So I assume you mean 20K units with the same ID, and 80 different IDs ? So 1.6 million total?
That could easily be within ASIC territory, as the functionality is so simple that even a tiny 4 bit MCU will have a lot of wasted die area.
Probably also worth investigating COB assembly.
Finding the cheapest MCU is probably the way to go, which would probably be mask-rom. I don't know the economics of maskroms these days ( and how they compare to flash or OTP) , but I suspect you'd want to have one maskrom and a way to code the ID on the PCB, rather than a mask for each ID, but if the cheapest MCU turns out to be OTP or flash ( or mask with some OTP) then code-per-chip type may be the cheapest route,
If you're wire-bonding a COB you could use the bonding process to code the IDs on identical chips.
4 pins with a hi/lo/open option gives you 81 codes, but you could also potentially share the LED outputs, e.g. 3 pins that can be bonded hi/lo/open or to one of the 3 LED outputs gives 216 codes.
You probably want to include some error protection in the code, depending on how critical error performance is - parity, crc, ecc. or if you will always be receiving multiple copes, simply requiring 2 or 3 identical codes.
Probably the main thing that will drive the design is power - what battery size, what life do you need and what options do you have to turn off/on or save power when not needed. Also what latency is acceptable, to determine teh transmit rate.
One option you have with IR LEDs , as they have low Vf, is to run from 1.5v, so one battery option is an alkaline button cell ( LR44 etc.) , assuming you can find an MCU that runs on 1.5v - probably doable for a maskrom part - ISTR Epson and EM Microelectronic do low voltage mask MCUs.
The advantage of alkaline is you can get a lot more peak current out of them than lithium coin cells, so will be able to pump plenty of power into the LEDs