Bumping an old thread here, but for the benefit of future searchers:
I had the exact same situation on my 78 SC, I could find no way of getting the bracket out with the studs in and the check valve in. However, it occurred to me that I could perhaps take the studs out first by double nutting them. The bottom stud was even hard to find clearance for with the check valve there, but it was possible. What I did was this:
Double nutted the stud, got it broken free enough that I could turn it by hand. broke the double nuts loose. At this point I couldn't remove them because there wasn't enough clearance, I had backed out the stud too much. then I hand-tightened the stud back in as much as I could to get as much clearance as I could. I suppose you could even use pliers here if necessary though you are likely to damage the stud, you are probably not planning to reuse it right away if you're removing this stuff.
Once I had the stud tightened in as much as I could by hand, I then had clearance to get the nuts off, and following that had clearance to take the stud all the way out by hand. The upper two studs have plenty of clearance, though one of mine was really in there. I was putting way more torque on the nuts to double them than I wanted to, but in the end I got it out without any stud extractor.
I will now need to replace the upper two studs (don't think the lower one does anything other than holds this bracket on) with 6x42 studs as described in this thread (Thanks Jim Sims):
http://forums.pelicanparts.com/porsche-911-technical-forum/101554-smog-pump-removal-what-length-chain-cover-studs.html
Again for searchers, Here's another related thread on leaving the spider in:
http://forums.pelicanparts.com/porsche-911-technical-forum/591373-safe-leave-spider-heads-without-smog-air-pump.html