The slimline converter was introduced around the time of the uber-thin Parker 180 (c.1975) IIRC.
I suspect that the majority if not all of the Parker models that followed were designed around the slimline converter and its similarly skinny descendants. The Parker 35, Parker 50, Parker 85, Vector, Parker 88/Rialto, Arrow/Parker 95 all will not take the broader converters, for instance (I have just checked). The barrel of the c. 1983 Parker Premier is broad enough to accommodate the wider converter but I wouldn't like to try my luck and tighten everything up!
The good news of course is that the narrower converters should be backwards-compatible thanks to Parker's forward-thinking many years ago.