Using acidic detergents
Many commercial detergents are composed of pH-neutral surfactants like alkyl polyethylene oxides plus alkaline additives like sodium silicate or carbonate or borax, which help dissolve greasy materials better than acids. 

There are some acidic detergents, like citric acid cleaners for stainless steel and other metals and toilet bowl cleaners. The acidic function is paramount, and the reduced surface tension is secondary, useful in providing better wetting.

It is instructive to consider what cleaning really means, and the individual steps that go on. First, water is the primary cleaning agent. It is the universal solvent, but not quite good enough or fast enough. So we add surface tension lowering agents - big improvement: oily materials are wetted and can be suspended better as the first step in removal. Alkaline additives then combine with polar surfaces to further displace oily materials, improving cleaning action. Acids don't help with oily materials much but can remove some contaminants better.

Dispersants for solids, like mud or clay, are typically anionic polymers, usually alkaline because the anion contains groups that will adsorb on polar surfaces and disperse the particles by electrostatic repulsion, assisting their removal.

There are classes of surfactants where the oleophilic group is anionic, like sulfonates or phosphonates, and these can be acidic if the cation is hydrogen or alkaline if an alkali metal, or nearly neutral if the cations are mixed. Another class of surfactants, called cationic, has the oleophilic group attached to nitrogen, and is typically somewhat acidic because the anion is the anion of a strong acid like HCl. 

So you could optimize your cleaner by selecting a pH of water that cleans best; then add a specific surfactant to improve removal of your specific dirt - or the reverse. And consider interactions and whatever other additives might help.