Unfortunately I have a very old digital camera and it did not want to focus. But the metering rod slides about a 1/4inch into the adjuster screw (you can kinda make out the wear mark on the rod). I imagine that this is a size for size or 0.001" interference fit when theses two parts were created. A slight interference fit would allowing them to stay together. But some how over the years either it has loosened up or maybe someone took it apart, but I just don't have enough interference to keep the two piece together. I can pull it apart with just a little bit of force.
Thats why I scrapped a screwdriver on the metering rod interference surface hoping to cause a few burrs that will act as a neural and create an interference between the two.
My thought on solder was to use the same technique as sweating a pluming pipe. Clean the end of the rod, put some flux on just the end, then install it into the adjuster screw, then heat the two pieces until the solder flows in between. And obviously check that it did not block the center passage.