Can someone clarify if the pole pieces actually screw into the magnet which the bobbin is attached to on a 1997-2015 era hi gain bridge bass pickup? And if so, do they go quite far into the magnet? Like half way down or what?

No. The button top studs are molded into the bobbin and have contact to the bar magnet. I found this out when one of my high gains died and I had to have it rewound. The rewound coil was find, but had reduced output. Upon inspection, it was apparent that some of either the glue holding the magnet to the bottom of the bobbin, or the potting wax of the rewind, had worked itself between the magnet and the slugs, breaking the direct magnetic connection. So I took the magnet off the bottom, scraped everything off of it, and carefully glued it back into place with full contact to the slugs.