The JP website (https://www.jprifles.com/buy.php?item=JPBC-9MM-SCS) states: "Reduced stroke length for faster firing impulse when used with JPSCS-9MM" - meaning it's the same stroke as a carbine spring and 9mm buffer. So yes, that's what will work with your BCM receiver extension with no extra spacers needed.

The weight of the JP buffer/spring should be sufficient, since you have a short barrel. The super-heavy buffers are necessary for longer barrels where gas blowback is happening for a longer period of time.