On the whole, it does seem that “tuna” is an American variation from British “tunny”, but as is often the case, the American word has displaced the original British one.

Not quite. Tuna is borrowed from American Spanish, which in turn is from the Spanish atun, which is from the Arabic at-tun, which comes from the Latin thunnus.

Tunny comes from the French thon, which in turn is from either the Portuguese ton or the Italian tonno, which are from the Latin thunnus.

Tuna is cognate with tunny, not derived from it.

Any idea how the “a” got from one end of the word to the other?