>The 'magic' ingredient which comes back in all methods seemes to be vinegar which neutralizes the sulpher<
Hildo, I did not notice this for some time. However, as a matter of learning, it is not correct.
The Salt Petre (KNO3, sorry but there is no subscript available) is oxidized mostly to Potash (K2CO3), which is a strong alkali. It is water soluble and effectively neutralized by the weak acid in Vinegar (Acetic Acid). There is also some Potash Lye (KOH) formed, which is a stronger alkali, but still washed away and neutralized by the Vinegar.
Some of the black powder substitutes are Potassium Perchlorate based formulations (KClO3), which ends up mostly as Potassium Chloride. Potassium Chloride is akin to table salt and will even rust under oil, sometimes. Although this is effectively removed by water, if left in the bore it is more corrosion promoting than the Potash. KCl, Potassium Chloride, is the same compound as produced by corrosive Perchlorate priming as used in smokeless powder military ammo. Lukewarm water, perhaps along with a mild detergent as a wetting agent, is the most effective way to remove KCl
In principle, since acid and basic conditions are dilution dependent, one should be able to remove water soluble alkalies from a gun simply by applying enough water--and that will work and easily, too. Soap helps break the surface tension, removing crud and allowing easier access to the alkali.
Apparently (I have heard but do not necessarily agree with) adding a BP cleaner with ammonia in it makes these conditions worse, especially with the BP substitutes. Although this may be observably correct, the chemistry that I have seen quoted for the phenomenon is suspect, I think.
Many people quote the use of Hydrogen Peroxide. It may very well aid in crud removal, but the Peroxide supplies added oxygen and promotes rusting on a grand scale. Avoid it like the plague.
Yes, I know that there are other things there, too. Things such as potassium sulfides, sulfates, sulfites, polysulfides, raw sulfur, and so on. However, the main enemy is alkali and or a salt, and water soluble at that.