Dialect and Finding the Right Word

To make sure I'm understanding you right:
Crashers speak "Basic" and land on a planet. They go native, and learn "Native." 600 years later, people who speak Basic arrive and may recognize the Crashers' speech as an archaic form of Basic.

For me, the biggest stretch is that the non-native language would be preserved, especially after that long a period. (In fact, it kind of smacks of imperialism.) If the natives are kind enough to adopt the Crashers into their culture, and the Crashers really don't expect to leave or meet anyone who speaks Basic again, why keep it? It would be one thing to staunchly hold on to your native culture/language/traditions if you're the last of your people and you want to keep that culture alive (like modern-day Native Americans), but presumably the Crashers are just a small group of a massive collection that speaks Basic, so there's no real need to preserve it for the sake of "keeping Basic alive." If Crashers are in such dire straights, I think they'd be more utilitarian than that.

But for the sake of avoiding universal translator cop-outs, I think the Middle English-y answer would be most realistic. Of course, if the original Crashers were handing the language down, it wouldn't just stay static and archaic, but might distort over time through teaching (like the game of "telephone") or evolve in its own separate way from the evolving language of modern Basic. (Two languages that share a common root language, but fork and develop differently over the next few hundred years)

My best suggestion: Get thee a linguist on the explorer crew. Universal translators are a cop-out as you say, but linguistic change is predictable and retraceable to a skilled linguist. Variances in pronunciation (phonological change) can be figured out and duplicated, and a linguist could be an interpreter pretty quickly. Then flash forward a few months and the linguist can help teach the rest of his/her crew the rules for adjusting to the alternate version of their own language.

A good example of all this is the linguist character from the movie Stargate. Check out the scene where he first starts figuring out how to adapt his understanding of the language for the variant version the 'natives' are speaking in that movie. He's tracking and documenting phonological change so he knows how to speak it. From there, he'd just have to learn new lexical items (in case they adopted a completely different word for things like "chicken", for instance).

Show us linguists some love. We make a whole lot more sense than magic translators or speakers understanding one another after 600 years of change.

Six hundred years for a language isn't very long. Middle English would be comprehensible for a speaker of Modern English, and similarly with French, German, Italian, and Spanish, and most other languages.

Are your natives literate? If not, that would be a very good reason for the continuation of Basic - it could become a record-keeping language like Latin was. Alternatively, the two dialects of Basic could sound so different that neither party can understand the other one, but the dialects remain similar enough that they can puzzle out each other's writings.

If the language of the marooned tribe was originally "galactic basic" then I wouldn't bother having the woman speaking haltingly, but have the newcomer recognize the construction and form of the language, as suggested by PeterL. 600 years isn't a long time for a language when there is some kind of mutual history between the original and the current (ie: English has been spoken pretty much consistantly from Chaucer's day to ours, which is why we can recognize it). However, 600 years in total isolation could drastically alter certain things, especially nouns. Your newcomer could understand the way the descendents of the crash victims put words together, but have trouble understanding some of the words themselves.