First of all, its a little cheeky to tell a fitter what he should be looking at, im sure he's capable himself, as sometimes its a game of discounting things to get to the real issue.
And.... without having to buy and fit every part possible to remedy the fault....That would be stupid, but some people do! You see it on here, people asking for advice and then listing 5-6 parts that have been fitted but not solved initial problem.
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Has he checked the boiler is'nt overheating.
Also has expansion vessel been checked (that its correct pressure)
You say aav is spitting? It sounds like the boiler its getting rather hot and its releasing from a already problematic auto. air vent. ( These always drip or hiss slightly) Pain in the bum sometimes.
The heat exchanger could be scaled up also, but you would only find out by removing, which is'nt feasable. You could check hot water flow rate at a couple of sinks to get a average flow and then check it against what the boiler should give.
Anyway its easy for me to fire of things to check while sitting behind a pc, but its another to be actually there dealing with the issues.
Hope its gave you a couple of things to go on