Vinegar does reduce the surface tension quite a bit. If you put a tablespoon or two of vinegar in a bowl and then run water into it, the bubbles that form on the surface persist much longer than they do if there's no vinegar present.
I suggest reconsidering your rejection of the vinegar recommendation.
Beyond that, airhuff's right -- you're searching for something that will preferentially accumulate at the air-water interface. Air is far less polar that water, which means that you need a chemical that has both polar and nonpolar characteristics. No small inorganic solutes possess appreciable nonpolar regions, and once you tack on a nonpolar tail of any substantial length, you're back under the umbrella of detergents/surfactants.
The foaming potential is absolutely a function of concentration, as airhuff says, so it's a matter of finding the right number of drops per gallon to achieve the balance of properties you're seeking.
UPDATE, 22 Oct 2023: As a practical example, Shin and Liu (2004) controlled the void size in bubble-microtemplated electrodeposited copper foams by tuning the acetic acid (vinegar) concentration.