Help with Application Decision

Hello everyone I’m stressing out right now because I forgot to sign up for the September LSAT last night. For context I have taken the test twice, scoring 165 the first time and 171 the second time. I wanted to know whether it is worth it to sign up for the October LSAT and push my application all the way to late October or just apply really early with my 171. For further context I graduated with a 3.945 gpa, I have 2 decent letters of recommendation, multiple internships, and tons of volunteering including a few leadership opportunities. I intend on applying to Texas, Vanderbilt, Duke, Northwestern, Virginia, Georgetown, Texas A&M, and Baylor. Is it worth it to attempt the test again in hopes of increasing a few points while trading away an early application? I would love and really appreciate any help🙏