You don't need LABC involvement to remove a stack and fit an AAV, so you aren't trying to get around any rules.
I'm not particularly concerned about such matters, but (really for the benefit of others) is that actually true?
As far as I can make out, with the exception of electrical work [which is now covered explicitly in 12.6(A) of the Building Regs],any other 'building work' is 'notifiable' unless it is listed as exempt from that requirement in Schedule 4. In that Schedule, even after amendment, it lists things such as replacement of bathroom items, work on cold water systems and replacement of gutters and rainwater pipes etc., is says nothing about soil pipes or drainage systems and, indeed, qualifies those exemptions with:
..... where the work does not include any work to underground drainage, and includes no work to the hot or cold water system or above ground drainage, which may prejudice the health or safety of any person on completion of the work
Am I misunderstanding?
On the subject of ventilation elsewhere, I don't think it's a deal breaker. If you fit the AAV and it works fine with no abnormal back pressure blowing traps then it will be fine. If there are issues you may have to look at a different solution, but are in no worse off position than when you started.
Again, is that necessarily correct?
As you say, in terms of 'air admittance', the situation is pretty straightforward. It either 'works' or it doesn't (in which case one would re-think) - and I imagine that it very probably
would 'work' initially, the issue being that the AAV may theoretically eventually 'get stuck' (resulting in water being 'sucked out' of traps etc.) - but, again, one would then simply review the situation, and either replace the AAV or move to a Plan B, if that situation eventually arose.
However, air admittance is only half of the story. Some people here have 'majored' on the need to allow the release of toxic gases from the drainage system - something which AAVs are specifically designed
not to do. That need can obviously only be addressed by open vent(s), in the same or other properties - which is a reason why it would not really surprise me if work on soil pipes etc. were 'notifiable'.
However, having said that, pragmatically I am very inclined to do as I originally suggested, and not lose much sleep over 'rules' or other people's viewpoints!
Kind Regards, John