I heard that years ago, they were talking about a mast mounted Stinger system for the Seawolf. I'd be interested in seeing any sources you have on this submarine mounted SAM system, especially range.
OK, some problems with your idea:
First, the range of the missile is going to be extremely limited--if by nothing other than the limits on SENSORS passing through the air/water interface. The only thing you're going to be able to rely on that doesn't involve coming to periscope/mast depth and sticking up the BPS-15 radar set will be passive sonar, listening to the noise of the aircraft on the ocean surface. That signal fades out very quickly as the target gains altitude.
Second, a SUBSAM doesn't NEED to reach up to 13,000 feet to bag an ASW aircraft; most ASW ops are flown at much lower altitude.
Third, the missile can easily generate what is known as a "flaming datum." In other words, if the plane manages to get off a warning that it's under missile attack, that area of ocean is going to suddenly have a LOT of ASW aircraft overhead, and any other ASW assets (ships and subs) will start closing in. A submarine's greatest weapon is its stealth. Once it loses that, it's in BIG trouble, as it has very few weapons available to it.