instead of using 8 thermocouple amplifiers before the 4051 - can i use 1 amplifier between 4051 and ADC and connect the thermocouples directly to 4051 inputs ?
(i want to ask if the 4051 disturb the millivolt range outputs of thermocouples ?)
look at noise and drift for your instrumentation amplifier and the analog switch. There you will find the answer to "will I meet my specs if I do so"

Erik