When Ovations first came out (was it in the '70s? or early 80s?), they were something entirely new, not only for their rounded plastic backs, but also because they the first and only acoustic guitars manufactured with built-in electronics. (Or, at least, the first to be widely enough marketed for me to be aware of 'em.) Perhaps that would explain why they would sound best when played through standard "electric-guitar" amps ~ there was no such thing as an acoustic-guitar amp at that time.

Built-in amplification in acoustic guitars is now very commonly available, under a whole slew of brand names. While it may once have made sense to look primarily at Ovations when seeking an acoustic ax with on-board electronics, it has been many years since a much wider variety of brands have been available for considerations, including (of course) many models with standard-shaped wooden bodies.

Have you considered installing a pickup in a guitar originally made as a straight-acoustic instrument, either a new purchase or one of your current instruments? You wouldn't have a hole in the side of the body to accommodate a switchbox ~ you'd have to rely exclusively on your amp's knobs for volume and other sound controls ~ but is that necessarily a bad thing? Anyone have any input about this approach?