One big problem with the Valiant is that even if she was launched within a few months of the Phoenix, she would only have a maximum of 2 years to reach the edge of the galaxy. Given that this is a trip of a good 1,000 light years of more, the Valiant should be able to average Warp 10 (TOS scale, warp 7.94 on the TNG scale). This is way faster than the ship should be able to do - hell, it's almost two TNG warp factors faster than a Galaxy class starships average cruise!
I can only think of two ways this could happen. The first is the 'warp
highways' theory - there could be 'spacelanes', naturally occurring stretches
of space where warp drive works far better than it normally does elsewhere.
This idea would also allow for oddities like the Enterprise-A's trip to
the centre of the galaxy in "Star Trek V : The Final Frontier". The other
possibility is that the Valiant encountered some sort of alien craft which
dragged it off at high speed - a variation on what happened to the E-D
in "The N'th Degree". Personally I don't like either of these ideas all
that much, but I can't think of anything else offhand.