Sulfates and persulfates as accelerants in black powder?
Sulphates and persulphates cannot be considered as analogues to chlorates and perchlorates.


Perchlorates are frequently used in professional pyrotechnics, being more reactive than nitrates.
Chlorates are too reactive for safe use.
Sulphates are useless as not acting as oxidant. 
Persulphates have limited oxidative oxygen content, compared to nitrates or perchlorates, but as chlorates are too reactive for safe operations. 


As a general rule, you must know what you are doing. More reactive mixtures may not only lead to faster wearing of the guns, but also to a gun blowing into your face.

Sulphur cannot be replaced by sulphates/persulphates, as it has the opposite role than oxidants. It would be like if you wanted to replace oxygen for breathing by carbon dioxide, as both contain oxygen.



Gun powder


  Chemical reaction
  
  Gunpowder does not burn as a single reaction, so the byproducts are not easily predicted. One study showed that it produced (in order of descending quantities) 55.91% solid products:
   potassium carbonate, potassium sulfate, potassium sulfide, sulfur, potassium nitrate, potassium thiocyanate, carbon, ammonium carbonate and 42.98% gaseous products: carbon dioxide, nitrogen, carbon monoxide, hydrogen sulfide, hydrogen, methane, 1.11% water.
  
  However, simplified equations have been cited.
  
  A simple, commonly cited, chemical equation for the combustion of black powder is
  $$\ce{2 KNO3 + S + 3 C -&gt; +K2S  + N2 + 3 CO2}$$
  
  A balanced, but still simplified, equation is $$\ce{10 KNO3 + 3 S + 8 C -&gt; 2 K2CO3 + 3 K2SO4 + 6  CO2 + 5N2}$$