BTW, I think one authority that is used to say that gerim say the same brochos is represented in Rambam Hilchos Bikkurim 4:3 (ruling that a ger says the parshah of bikkurim b/c Abraham is his spiritual father).
KSA doesn’t seem to rule on the children of gerim explicitly, so I don’t know what he would rule. Nire-li, if there is a doubt whether “L’Yisrael” would be yotzei, but “L’Avoteinu” would be yotzei either l’chatchila or b’dieved, a child born to a ger should say “L’Avoteinu” even based on the ruling in KSA (and of course this probably would also satisfy the opinion that everyone must say the same thing).