LOAF's list distinguishes between classes and types. "Class" means that all similar ships are officially referred to as belonging to that class. "Type", on the other hand, means that we don't know the name of a given ship's class, but we know that it's the same class as another ship. In that case, LOAF uses the first ship in alphabetical order to refer to all the other ships of this unknown class.
In the case of those cruisers... well, I don't recall what LOAF wrote in his list, but if he refers to them as Agincourt II, he doesn't say Agincourt II class, just that they're Agincourt II type. This doesn't mean that they're not Tallahassee class - it just means that we don't know for sure, so it's best not to assume anything.