>Meaningful truths about nature can be arrived at within those frameworks as is proved every day by physicists.

Ofcourse. Meaningful truths. Not absolute. Check the link about the video how one can demonstrate the earth being flat (using physics).

>There always exists the potential that one or more of the axioms is wrong, but that does not invalidate the internal consistency of the reasoning. One way I like to express this is with the thought experiment that our universe is actually an alien's dream.

That's a different story but first you need to be able to falsify the premise about the alien's existence and whether or not they can dream. 

>Does that invalidate all scientific knowledge? I would say that it doesn't. Our observations about how the universe behaves remain true, it's only the context that has changed: They are now observations about how the alien's dream behaves, rather than behaviors of an actual universe.

Of course not. Science is the greatest tool we have. 'Perspective' is the key word here, not the validity of a premise.

>Providing those behaviors remain consistent from one moment to the next, it is possible to begin describing them and building a model. That model is nothing but a reflection of what it describes. Even if we are mistaken about the true nature of it, the description of how it behaves remains accurate.

Indeed. Depends on the methodology upon the model has been build. A hammer will see everything as a nail. When it comes to humans, we are bound by a teleological hell that everything exists and revolves around us. The evidence though that we have is that everything always existed and rather recycles itself. This is of course a harsh truth to digest, hence the false premises about the nature of our position in the cosmos.