I'm reading up again to refresh my relativity knowledge. Though:

> even though near the speed of light, more and more of that energy goes into higher mass and slower time?

This to me does not sound very different from saying the (relativistic) mass to be accelerated is larger, and is what's stopping a 1G (or any constant) acceleration to be maintained to bring the ship to the speed of light.

The concept may have been an overly simplified pedagogical tool though that I need to upgrade from. (I'll keep the comment chain intact since it's educational to me).