Well, both the Excelsior
say "First Starship of Her Class" but given that both of these are a different style from the TOS style plaque, I don't consider this an invalidation of the other theory.
Besides, you can hack that up and make it "(First) Starship (of her) Class."
Hmmm, That could be a good alternative. I'll have to include that as an option to my answers for what class is the TOS Enterprise?