My UGPA is 3.8, but I failed a class, so my LSDAS GPA is more like 3.65 (I didn't take a ton of credit hours in college). I also retook another class, but from what I understand, this won't factor into my CAS GPA because the original score has no associated credits on my transcript. If I'm wrong, then my CAS GPA will likely be something like 3.59/3.6.
I had a legitimate personal reason for failing the class, but I'm not sure I will be able to convey this to law schools, especially because my grades in the other three classes that semester were As.
I just took my Diagnostic and scored 158. I missed 7 in RC, which is a bit concerning because I'm a slow reader and this is the most difficult section to improve. However, from what I can tell perusing TLS forums, I have a legitimate shot at cracking 170. I plan on taking the LSAT in September, but might push to December if my PTs aren't sufficiently high by the registration deadline.
Assuming I score 170 (I understand that's a big assumption), how realistic is it that I'm accepted by a T14? I figure Yale, Harvard, Stanford, UChicago, NYU, and Columbia are off the table, but could the other 8 be in play? How does this change if my score is 169, 168, 167, etc?
I have a few things going for me (see my softs), but they're probably outweighed by the fact I'm a white, heterosexual male and that I attended an average LAC in the PNW, which is respected regionally, but carries no weight nationally. Not to mention that, oh right, I failed a class!

Any insight would be great! Thanks in advance.
Here are my Softs: (Do these matter at all?)
1yr work experience in management consulting (will be 1.5 by the time I apply)... graduated Spring 2018.
Extensive volunteering for non-profits in my resident city. ~5hrs/week for a year now, will continue through application cycle.
Published in a peer-reviewed Economics Journal
Honors in Economics during undergrad.