This is an interesting thread. I've used APHS on and off for years in pinhole cameras and as an alternative in LF lens cameras.
I've experienced the same cloudiness issue, and this is what I've done to solve it:
1) Development time must be at least 1:30 (for Agfa Neutol WA diluted 1:10.) Any less time than this and it will risk being uneven.
NOTE: My initial tests with APHS proved excess contrast as a continuous tone film for scenic exposures, hence my initial reaction was to reduce development time. This does not work with APHS; instead, you must either choose a low-contrast developer (Soemarko, for example) or dilute the developer more and extend the development time.
2) Agitation of the chemistry directly above the center of the sheet film, as it sits in the tray, using the print tongs. I develop face up in trays. Using the print tongs, agitate the chemistry periodically, in a random motion, to ensure fresh chemistry is getting to the film's surface. I don't know if the problem is related to what is called "bromide drag", but perhaps some molecular compounds are coming off the film as a result of the development process and restraining the developer action. Perhaps a vertical slot processor could be used to verify this theory.
3) Presoak to remove the antihalation coating. It's hard to see the irregular development streaks under red lights or while in the developer under normal circumstances; even worse when your developer solution turns darker color due to the antihalation dye tinting the already dark mixture even darker. For sanity's sake I presoak, thus can reuse the developer with little concern for dye buildup in the solution.