One thing we know. If you have p-aminophenol and a strong alkali like KOH or K2CO3, you can develop film. Of course, without sulfite it will be grainy and lack film speed. Or will it? I tried this combination with 500 ml water, 1.5 grams p-aminophenol base, and enough of Sandy King's 75% K2CO3 part 2 to dissolve the p-ap. 8 minutes, 68 F, EDU 400 Ultra. The result is attached.
You will not see anything in this very rough test that you would not see in a Rodinal test using the same scene. What happened to the grain and all the other problems you might have expected from such an unadorned developer solution? Surely, you wouldn't expect to be able to make a long lived concentrated stock solution with just these two ingredients, but there are other ways to preserve solutions of p-aminophenol. One is to dissolve it in glycerine or in propylene glycol, and keep a bottle of Sandy's B solution handy.
I know for fact that at least 36 grams of p-aminophenol are soluble in a liter of either glycerine or propylene glycol. I have used either KOH or the carbonate with both of them, addig sulfite or not to the working solution. If I keep the sulfite to the proportions you would get by putting the suggested 384 grams in the stock, you would have only 7.7 grams in a liter of working solution. Seems hardly worth the trouble if you don't need it as a preservative for the stock.
You can get a handy little 4 fl. oz. bottle of very pure glycerine at most pharmacies to play with. 9 or 10 grams of p-aminophenol will go into that with a little persuasion in the form of heating and stirring.
How much Pyrocat "B"? Some must go into forming the potassium aminophenolate, and some more into raising the pH to a decent working speed. My rough test used 5 ml when I diluted 10 ml of the p-aminophenol solution with 50 parts of water.