the belt method could be done in a number of ways. I assume it can't be restrictive. the antistatic conductive foam has variable resistance when you compress it - use a divider into a comparator. or use a photo interruptor in a sleeve. chest expansion pulls a blocking "paddle" out and a spring/elastic helps it to return. Maybe even a simple contact that expansion separates and a spring/elastic returns (or the other way around). Or use capacitance between two plates that slide against each other - the greater the expansion, the lower surface area in common and the lower the capacitance. measure capacitance via an oscillator or directly measure V rise time across the cap. Or maybe use an accelerometer (seems overkill). Or a strain gauge. Or...
Then, it's just a case of reading the output of the sensor and rejecting impossible data.
edit: the baby breath monitor seems to not monitor respiration but activity. It's a pad that goes under the mattress. Even when quietly asleep, a baby has some movement. no activity for 20 seconds and they trigger an alarm. I assume they have some sort of cutoff if the crib is empty. Must be pretty sensitive. I think it could to be too sensitive to use on awake people.