You ought to determine where the trapped pieces are: is it near a tube?
I had the same problem, after I soldered fittings on the tubes of my 2-304. Yes, I cut off those silly extensions. All I had to do, was shake the core, but it took a solid minute of shaking to get it out.
I could have simply pulled the bits out, because I trimmed the tubes to about 1/2" in length, and I could easily see/reach inside.
BTW, the trick of filling the core with water, when soldering something to it, works great.
