What's the diameter of the Parker refill? Could you modify the SL to use the Parker refill, or won't it fit inside the SL tubes?
EDIT: Sorry, more correctly, could you make the PENCIL version of the slimline use the Parker pencil refill - I assume you'll want to take advantage of the SL transmission and not monkey with that aspect of the design too much.
EDIT 2: For example, could you turn a small, conical insert that would go in the SL cap, and attach it to the finial using a spring (MAYBE gluing the spring into place)? I'm not sure whether you'd get enough friction to turn the Parker refill or not. Otherwise, you could try using a slow-setting glue, and simply resting the insert on the top of the refill (on top of the twist mechanism), then sliding that inside the barrel. Sorry if a) this doesn't make sense, or b) isn't practical; I'm at work and THINK I remember what the Parker-style pencil refills look like and how they work.