@jblair814 He needs instant and proper feedback on his play bites. Your yelp feedback could work to an extent. Make sure it's instant and maybe a louder shriek than what you're already doing? Next best thing (and you'd have to make a call on this slight risk) is to take him to training class or a dog park to play with other dogs. Dogs play bite and give feedback faster and much more frequently than a human can in the same short time window. People may have mixed views on this but consistent socialization early on is important.
My pup was biting hard as well and dog parks fixed it pretty quickly. But when when he hit adolescence he got slightly aggressive to some (not all) dogs so I stopped taking him to the park just to be safe. But at least he learned to play bite properly during those few months and still knows how when we play wrestle.
I'm iffy about the time out thing. I understand they can be stubborn. We used our laundry room as a time out and one time he shredded what he could and pooped everywhere. Luckily he wasn't traumatized because there are times he sneaks in there without us knowing then when we shut the door he's alone in the dark but when we eventually find him he's calm. But he was traumatized from using his crate as a timeout (now he aggressively resists going into any crates). They can be touchy so be careful with timeouts yet they need to behave somehow. Rock and a hard place.