I had a SAP issue myself...car would stall when starting. For me, it turned out just to be that the hose from pump to valve had a hole in it (suspect from sucking in vapor with oil in it from leaking vcg...but in any case a hole in that short hose (my hose was rubber; yours looks like a plastic one similar to ccv hose)...anywho...
I removed hose, noticed a ball of gunk had lodged in the inlet to valve...pulled out gunk with dental pick, put a little dab of rtv on the vac line leaving the valve where it had cracked a tiny bit...and all was good.
Oh, I also removed the cover of the pump (three tabs)...saw that the filter was also a little gunked up with oil too...but since I couldn't find just that part I left it...but I had also read of some guy who shot WD40 through pump to clear things up...I wasn't sure if that was a good idea or not, but I did it too...actually, before I replaced the hose...for this lube job...I removed hose from valve, turned on car, sprayed wd40 into pump (with foam filter removed) and aimed the other end of the hose away from car (coz it was spraying wd40 around).
Anyway...that was about a year ago or more I think and I'm still on the road!
Just giving guys something to try before giving up on both pump and valve.
I actually have the new gasket for the valve, but haven't bothered replacing it yet...it's seeping oil a tiny bit (don't tell anyone)...but didn't have right tools to get in there and didn't want to start removing stuff just for that. Now I know how, so thanks for that!
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Mangofy your E46!