Looking at the schematic and seeing all of the not-connected pins made me moody.

It turns out that the ATTiny4313 is an almost perfect fit for this project. It has a 16 bit timer with input capture, a USART, a watchdog timer, can run with an external oscillator clock input, and will run at 10 MHz (this used to say 20 MHz, but it turns out that was wrong) at 3.3 volts.

I've already ordered boards with an ATMega, but I've already written new firmware that compiles without the Arduino IDE (with just the GNU AVR toolchain and AVR libc). Converting that over to using an ATTiny4313 was just a matter of reassigning the appropriate pins and renaming some of the registers.

If this prototype run works, I'll get another run made with the ATTiny SOIC footprint and test that out. Assuming that works without any big problems, then that will be the way forward.