IGNORE THE READINESS MONITORS. When you Reset the codes, all monitors begin again. They do not get to Ready for several drive cycles. Just because they are not ready is meaningless, EXCEPT that if they are not ready, you cannot get your car smogged. If you reset codes, the monitors do not come to ready for several drive cycles. If you check codes again and again, and reset each time, then the readiness monitors will never complete.
The SAP does nothing for rich or lean. The _only_ job of the SAP is to provide fresh air to the exhaust stream to assist the CATs to do what they do before they come up to operating temp. The SAP turns off after 120-ish seconds, and it only comes on with Cold Engine Start. Rich and lean are conditions that exist long before the exhaust gets to the CAT, and I don't even think the car's computer looks at rich and lean while the SAP is supposed to be running. CATs don't work well when cold, so the SAP was added to help reduce emissions immediately after Cold Engine Start. The SAP is not part of the Rich condition. Period.