the instrumental used in the end credits (which I rarely heard during the initial run because they'd cut the end credits and show commercials over top of them IIRC) should have been used
I've posted this elsewhere, but Archer's Theme (the piece you're referring too) along with the traditional Trek monologue by Bakula as Archer, was once released on StarTrek.com back while ENT was still on the air (or shortly after it was cancelled), so I believe it was initially considered, but execs at UPN wanted a pop song to catch the attention of a new audience.
What about the OFFICIAL Star Trek song, instead? The very same one penned by Gene Roddenberry, himself. Set to appropriate music, who knows? It might've even received an awared. At least it's not too late ... that can still happen with the next series.
It was not penned by Gene Roddenberry. Alexander Courage wrote the original Star Trek Theme. Roddenberry later wrote lyrics, ensuring he received royalties for the song rather than them all going to Courage.
For more info: http://en.wikipedia.org/wiki/Star_trek_theme#Lyrics