Read Quadrature encoders over I2C bus
However, I don't have a microcontroller on the remote PCB.


So put one there!
It is exactly for this type of application where tiny micro controllers are great. There are lots of 8 pin chips which are far, far cheaper then the $10 you mention. You can even implement 10, 12 or 16 bits if you want and have a choice of interfaces you can use to send data upstream.