You got me thinking after you mentioned the AAV's Looking at the one at the boiler am i right that the AAV should be on the pressure side of the pump?? if that's the case its on the wrong side. I assume to close them its just a case of screwing the plastic cap in??? it appears that one is closed so whether he just fitted it to bleed the system I've no idea. kind off defeats the purpose of having it??
AAVs can admit air as well as vent it.
As mentioned by another poster.
High up ones are more likely to be worth investigating.
Negative pressure on suction side of pump can pull air in via them.
IIRC you mentioned getting lots of air in the system... It could well be via the AAVs.

