The sulfite should dissolve readily. The p-aminophenol should not. If it did, it would be a sign that you had used p-aminophenol.HCl. This can be done, but will require different proportions. The hydroxide might be partly K2CO3 due to exposure to atmosphere.
The hydroxide converts p-aminophenol base to the potassium salt which is water soluble.
After I read your post, I retreated to my dungeon and made a batch of EZ-Rodinal. I had less than a teaspoon of sediment after stirring a few minutes with a soupspoon (my recently discovered automatic stirring machine). I tested it on HP5+ at 1+25 dilution according to instructions on an old Rodinal container, with proper results.
If through some accident you had used the p-aminophenol.HCl, the proper cure would be to double the amount of KOH. If the KOH is weak for one reason or another, the proper cure is again more KOH, but not so easilly determined. Perhaps the reason for the titration in older recipes was the uncertainty of purity of either or both p-aminophenol and KOH. You could not go wrong by adding more KOH to see if more of the sediment dissolves. It runs in my mind that a saturated solution of KOH will hold very little K2CO3, and will have a concentration that depends on temperature. If you make such a solution at a temperature higher than you are likely to have while working in your darkroom, and make sure it has an excess, you can use a table from the CRC Handbook of Physics and Chemistry to calculate how many ml of this solution will contain 19.2 grams of KOH at the current darkroom temperature.
You could try filtering out the precipitate and testing the clear liquid as if it were Rodinal.