Matt's Cutlass did this. Just got it all together with the new automatic, about 30 minutes of runtime, it started popping through the carb. Pulled a valve cover and found this. One on the passenger side had already ground off the tip of the pushrod too.
Weirdest symptom ever. Car ran fine, then all of a sudden without warning began popping out the carb. This is an exhaust valve, so the compressed cylinder was back-feeding into the intake. It was infuriating because we'd JUST gotten the car back together with a new transmission after sitting since November. 30 minutes of runtime later and this happens!
Talked with a few folks and they think this could be oil starvation at higher RPM. That would make sense. Engine doesn't make more than 40 psi and owner loves to buzz it to 6k. That's how a 5 speed got shredded too.