I'll add another wrinkle: Even if we assume the S.S. Valiant was only capable of Warp 1.0 typical cruising speed, this does not mean she was limited to "lightspeed" (1c).
I'm a big fan of STAR TREK MAPS
, whose INTRODUCTION TO NAVIGATION: STAR FLEET COMMAND booklet contained a detailed discussion of warp drive. The theory behind warp speed described therein is that faster-than-light velocity is affected by the spacecraft's environment, all the way from minor galactic "trade winds" up to dangers that represent fatal risks for travel ("there be dragons!"). So even a Warp 1 ship should be capable of reaching (at least some point along) the Galaxy's edge in weeks or months rather than years under what is called "Cochrane's formula".
I am fond of thinking that the Enterprise and the Valiant were stopped at the negative energy barrier because "Cochrane's variable", the effect that the environment has on warp speeds, was so great that it caused the engines to burn out. This is not discussed in the booklet, but it seems the phenomena of dark matter and dark energy would perfectly complement the "Cochrane's formula" concept.