26 m^3 of tungsten is what, less than a 3x3x3m cube? If they stack 10 cubes at the bottom they get mostly the full storage (-3m at least) for each weight. Seems feasible.
https://www.metalary.com/tungsten-price/
2000 tonnes of tungsten is 60 million USD, of iron is 200k USD.
Lead goes for around $2k/ton, so this might be a more feasible compromise.
Civilian sales look at least possible, I heard of at least one sailboat with a DU keel.