Simple test for the SAP check valve vacuum hose is to disconnect the small vacuum hose at the SAP check valve and either blow into the hose (you may need another length of hose and a nipple) and/or connect a hand vacuum pump up to the vacuum hose that connects to the SAP check valve.
You should not be able to blow/move air in this section and/or it should hold a vacuum. This hose has and electric check valve at the other end near the throttle body.
If you can blow/move air or this line does not hold a vacuum, it has a leak. Most likely the hard plastic pipe around the valve cover is broken on the bottom where you cannot see it?
Note this line only has vacuum applied for the first 90 seconds on cold start up. So if you car runs fine from 90-120 seconds and beyond, I would think this is a likely source of your problem.
Would like to hear back what you find.