However considering that a ship from the 1999's has nowhere near the capability of coming close to light speed
Well, DY-100 might well have that capability for all we know. There are no massive fuel tanks in evidence: even if those sixteen containers, of which five remain, are fuel tanks, they won't defeat the rocket equation unless we assume the engine to be supernaturally good, and after that we really can't limit our thinking to "can't reach 90% lightspeed in mere weeks" or the like.
Basically, we can assume that it would take at least several weeks and preferably months for DY-100 to do an Earth-Mars run, or else there'd be little need for cryosleep. Months would be better, because that would leave room for the known 2018 improvement after which Ares IV and her ilk could do the run in weeks. So, what does that mean?
Months to Mars could still be done with "traditional" rockets making one hell of a launch burn and then Hohmanning their way to Mars for a second such burn. Weeks would probably require some sort of a constant-thrust engine. And if that engine doesn't have outsize fuel tanks (difficult to tell, but if Ares IV had those, where were they? She'd need some for the return, too!), then we're talking constant acceleration at low fuel costs and thus very potentially spelling "interstellar".
Which leads us to "Space Seed" where two-three centuries clearly took Khan far away from Earth. Give him an engine doing 0.45c and he can turn the objective 270 years into less than 250 subjective ones, making the claim about him sleeping for two rather than three centuries truthful. In which case he's 100+ ly out already. And that only requires him to maintain one-gee thrust for less than a year, then coasting.
That's one way to estimate minimum performance for DY-100. Perhaps the
Valiant wouldn't get out to the Galactic Barrier in that time yet if being pre-2018 and therefore not entitled to performance better than DY-100. But she could arguably get there in the time allotted at any point after 2018, if we go by that 500 ly approximation (far enough that it's still the final frontier for Kirk, close enough that Kirk can get back from there within a few episodes, and perhaps the closest place for encountering this fictional barrier without it being obvious to the astronomers of Earth today).
Timo Saloniemi