Jon:
Well, I did some research. Tungsten *electrodes* (not welding rod, my mistake) are available in 10-packs for about $30 at welding supply stores, in several diameters, about 7" long. Found here:
They are for TIG welding (tungsten inert gas) also known officially but not really to anybody as GTAW (gas tungsten arc welding). (GTAW and GMAW are 'more neater' acronyms for TIG and MIG welding, but the problem is you just can't pronounce 'em as nice.) TIG welding uses a 'nonconsumable' tungsten electrode torch, a shielding gas like MIG welding, and separate filler rods made of the weld metal. It's very common in industry.
Pure tungsten electrodes are available, as well as rods mixed with thorium (radioactive) or nonradioactive rare-earth metals to retard evaporation and increase conductivity, neither of which is important to us, so the pure W is better. It can be cut with normal HSS tools. Solid tungsten has ~1.7 times the density of lead; I did some quick calculatin' and a close pile of 1/8" diameter electrodes will have 1.5 times the density of solid lead or 2.2 times the density of solid steel or zamac (which are similar in density).
Incidentally, a similar close pile of 1/8" diameter solder has 1.3 times the density of a solid chunk of steel that fits in the same place.
Hmmm....Osram Sylvania, the lightbulb people, makes W rod...
Now this might be a better supplier:
Cordially yours: Gerard P.