It seems like the MCP3426 is only capable of 15sps at 16 bits resolution though.
I'm curious if the 100-200sps is an actual specification or just a number drawn out of the air, perhaps 10sps is enough in reality?

I stumbled upon the AD7680. It's "driven" by the SPI-interface clock and they claim up to 100ksps when clocked by a 2.5MHz SPI clock.
Given the required 200sps the needed SPI-clock speed is way lower so SHIFTIN should certainly be an option. And it's a availble in a 6-pin SOT23 package.