Further, if I do (D) or (C) and empirically discover dependency, I should then disregard the LRT p-value and rely on an alternative, possibly the robust score test. And I should also test for serial dependence and possibly implement an AR(1), correct? Sorry this is so condensed. I wrote a longer answer initially, but I suppose short answers are encouraged. And I also wanted to reply quickly, although I haven't found the time to engage with all of your sources yet. I will, though! Thanks again!

Thank you! I appreciate the effort that went into this reply. I have some follow-up questions but I’ll try to keep it brief due to the character limit: Am I correct in my understanding that (A) the LRT is valid for evaluating the overall significance of the predictors + random effect, but (B) the significance is often inflated in cases of within-cluster dependence (which my data most likely have)? Should I: (C) investigate the dependency empirically or (D) simply assume dependency on theoretical grounds? For (C) could I compare a full model with and without the random effect with an LRT?