When are you planning on taking the test? The more you practice, the closer your timed score will get to your BR. Taking a timed test opens up a lot of room for errors that you wouldn't make if you didn't have that additional pressure. If you're satisfied with your BR score, you can probably reach that score if you just continue to practice more.

If you want to score higher than your BR, you may want to look at what conceptual areas you are having trouble with and review those parts of the CC. Make sure you understand why you got the questions wrong. If you're still not sure, someone else might be able to provide clarification.

The LSAT asks you to conduct a few very specific types of reasoning. I'm sure you'll continue to improve as you practice more. Good luck!

Premise: "people of different cultures identified the same emotions in photos"

conclusion: "this is due to a genetic predisposition."

The assumption is an unstated premise that necessarily links the conclusion and premise in a way that if the assumption is true (and it is not always true, so this can be a trap), the conclusion logically follows.

The necessary assumption in this argument is that the phenomenon described in the premise is due to genetics and not due to cultural factors.

A, B, and E do not provide this link. They are actually irrelevant to this. They don't explain how you could get the conclusion from the premise.

C actually goes against the conclusion, since it acknowledges cultural factors, whereas the conclusion denies them.

D is correct simply because it is the only choice out of the five options that could actually lead to that conclusion logically following from the given premise.

I somewhat understand your reasoning, but the necessary/sufficient issue and probabilities are not relevant here, since none of the other answers meet the requirement of the correct answer by linking the premise to the conclusion in a way that logically follows.

I hope this helps somewhat. Let me know if it doesn't, and I will try to better articulate it.