But they are all pressure driven, not a contact microphone like the EAP.
Those other transducers are no more pressure driven than is the EAP if, by that term you refer to air pressure, as is the norm. All the transducers mentioned are driven by mechanical vibration. By the way, the EAP can hardly be driven at all by air pressure. I tried by exposing it to substantial sound-pressure level in a laboratory setting. That makes sense, given that it's a contact microphone. It must be in mechanical contact to receive the vibrational energy via the solid media. Again, that's a characteristic shared by the other piezo transducers mentioned.