Many companies (i.e. biotech companies) have aqueous holding tanks to automatically adjust the pH of these tanks prior to release into the city's water treatment system. For increasing pH, soda ash (sodium carbonate) is typically used while for lowering pH either Alum, Citric Acid or Acetic Acid are typically used.
You could also use dilute sulfuric acid to neutralize your tank. It is corrosive and will require PPE and good safety procedures. It has the advantage that the resulting salts are highly soluble in water and it is cheap.
Some other considerations...
1. This tank should be agitated or stirred.
2. You will need some sort of pH measurement
3. You should determine the number of equivalents of acid needed. This will determine the amount of acid needed which may limit the acid you choose.
4. Neutralization of a "soap" may result in the formation of insolubles. Even if your tank has a pH of 12, you will get localized areas of much lower pH as you add the acid. These low pH areas may result in the precipitation of the soap.