Roger, like you I am not an expert in this. So I am speculating here and bear in mind my newness with the process. I would think that the brown spots are ferrous metal left over and that you need to fix just a tiny bit more, since this only happens to you with kallitypes and the only difference is the need to fix. You might also want to try developing a little longer, remember the developing time is essential for kallitypes as it dissolves all the ferrous metal left over. If I were you I would try developing a little longer first, if that does not work then try the fix for a little longer. I think you will see better results with PO, faster speed and better highlights IMO.
BTW I missed a not in my previous message, it should be do not add ammonium to the thiosulfate as it bleaches the print