The experiments at LUX and Xenon500 have all but ruled out particle form of dark matter. If DM exists in our galaxy and interacts with matter, we would have seen it by now. Also, there have been several studies recently confirming that the Higgs particle found in 2013 is the Standard Model Higgs, which pretty much shuts the door on SUSY (unless we redefine SUSY to be any particle that is just beyond the energy level of our accelerators - which seems to be the fashion). I can theorize that it's purple unicorns that makes objects in galaxies spin faster. Since the probability of a dark matter particle is quickly approaching the probability of purple unicorns, when is it appropriate on this Q&A to ask the question: What other models would explain our universe?
This isn't the Physics Forum, it's Physics Stack Exchange.
Anyway, you've got two things going on in this question. First, you are presenting evidence to support the claim that dark matter is ruled out.
The experiments at LUX and Xenon500...
...is quickly approaching the probability of purple unicorns
None of that is relevant to this meta post.
The second thing you have going on is
...when is it appropriate on this forum to ask the question: What other models would explain our universe?
In the sense that you probably mean it, never. This site is not the place for a comprehensive listing of models that explain anything.
What would be reasonable, I think, is to ask what alternatives to a certain model exist within mainstream physics. In other words, you could ask what competing explanations are being seriously considered and actively researched by the community of scientists in the field. Of course, this requires you to (1) know what you're talking about well enough, and (2) do enough prior research, to establish that there are competing models within mainstream physics. If you ask about alternatives to, say, quantum field theory, it's not going to go over very well. (Actually I'm not sure that's true; it's not my area, but perhaps there are competing models that are actively being researched. But it's about as well established a theory as I can think of at the moment.)