I really can't say how any oil can really clean existing deposits or varnish other than VRP. Everything else has been anecdotal and based on limited information. You need a specific aniline point to clean and many POE and adipate esters have great solvency. AN is also a base oil that adds solvency, so it could be why HPL appears to have better cleaning ability. However the amounts used would also play a part in whether it runs clean or can clean/to what degree. I don't know what Amsoil uses they don't say anything anymore about base oils. HPL also has high detergent levels. Only a chemist or formulator could likely answer this question.
Valvoline was one of the first to actually develop an oil specifically designed to clean with their VPBR oil. They worked with Cummins on it so they're very familiar with what it takes (see their patents). Consider that VPBR is 50% POE, however it's only to be used one time. So in theory you'd think HPL/SS would clean over time as well. Oddly enough Dave G from RL said RL would not clean but run clean. I believe
@JAG said that RL did not clean in one of his engines.