Reviewing the TEC chip data sheet, it looks like it should be possible to swap out the resistor dividers and PID network components for an ATtiny (I2C slave) and x4 DAC (SPI). A thought triggered by seeing this module from Thorlabs OEM Temperature Controllers in SMT Packages.

The voltage and current limiting functions can be accomplished using a DAC to set them (ILIMC, ILIMH & VLIM), with the last channel controlling the output (OUT2).

This would allow the PID to be carried out in software and allow an adaptive algorithm to fit the thermal behaviour of the controlled mass. The controler has a linear response for control voltage of 0.25V to 2.25V for control signal of +5V to -5V on the TEC.

Voltage, current, status & temperature monitored by the ATtiny 12bit ADC, which should have sufficient resolution?

I'm looking at the ATTINY816 (at $1.06) and MAX5715AAUD+ (bit pricey at $5 in singles)