That’s what I’m seeing too. The only engine available for '05 in the Cav was a 4 cylinder 2.2L VIN F, not a 2.4 L. Seems to be the case for the 03 and 04 Cav too, the 2.2L is all they offered. I don’t see mention of a Cav even offered in 2006. Maybe they brought it back later.
It still might be possible OP to do what you want, but you’ll need to ask someone who’s either done it or tried to do it, someone in the know in other words. One idea, there’s a magazine titled Chevy Performance, something like that. Pick up a copy (my Barnes and Nobel carries it) and phone some of the pertinent advertisers, maybe they’ll be able to steer you to somebody who knows.