For this kind of project, I'm not convinced that there's a whole lot of difference between the AI and LABC routes - but I'd be interested to hear others' views on it.
A lot of AIs used to be LABIs and there's a general impression among the AI community that when becoming an AI was made possible, many of the LABIs worth their salt did just that, for reasons such as they were attracted to a greater variety of work, more money, closer customer relations or didn't like council mindset. Apparently then, that leaves behind people who for one reason or another didn't want to jump ship, the general perception being that they were either close to retiring and didn't want to jeopardise that or they just couldn't hack it out in a competitive commercial world. Ask your AI a bit about his work history; if he's ex council, ask why.
I'm ambivalent. In one county south of here I'm on my second house with the same council inspector and he is absolutely fantastic, helpful, looks for solutions and saves me money nearly every time he walks onto the job. In another county I've got an AI who is brilliant, old school and interprets the regulations and law in a very sensible fashion and I'll probably use him again because he crosses many county boundaries in his working range.
Ultimately there may well not be much difference between AIs and LABIs, though you CAN choose your AI, but if your money goes to the council they seem to choose the person you'll work with. If nothing else, this could be the most significant difference on any project