In general terms, TOS makes it clear that the warp engines are capable of very high speeds even when carefully designed not
to be. Supposedly, warp eight for the Constitution
class means redlining the poor bairns, and isn't recommended for any length of time - yet warp 14+ can still be achieved, simply by sitting on the safety valve.
It wouldn't be at all unexpected, then, for the Valiant
to be briefly capable of, say, warp ten. Or even more briefly, of warp fifty. The relevant question then becomes, does speed times duration give the distance necessary for going to the galactic rim at any value of speed or duration - or do high speeds always blow up the ship too soon?
The bounce effect of the Barrier sounds quite plausible. It's probably weirdly directional, too, so that you can end up bouncing like a flipper ball inside
the barrier basically forever unless you know which direction to push ("Is There In Truth") or happen to guess right ("Where No Man").