I don't agree with the statement that water-quenching does NOT increase their hardness. This may be true of pure lead, or perhaps even nearly pure lead alloys (1:40 tin:lead?), but it is not true of Lyman #2 or "Hardball" alloys. I've tested this myself, and not with a reloader's hardness tester, but with a full-size industrial-standard Brinnell Hardness tester.
I'm not sure of the minimum wt./wt.% of antimony is necessary to "heat treat" projectiles, but 0.25% arsenic seems to be enough. Depending on the process involved, 0.5% is sometimes used. Whether arsenic in an alloy that is free of antimony will heat treat is unclear to me, but on a guess, I suspect it would work.