Top Ten possible? 700 GMAT. LGB(T)

I was wondering if I could get some help in deciding which schools I should strive for and how revealing I should be in my b-school applications. I was laid off from my petroleum engineering job 6 months ago and after having trouble finding a job have decided to pursue my MBA.

B.S. in Engineering from Texas A&M University- 3.0 GPA
GMAT first take- 700 (Have scored a 720 on official practice test)

Job description- I worked as an offshore petroleum engineer for several years in the Gulf of Mexico on the rig and also spent time in the office writing operations programs and cost projections for >$70MM dollar projects. Three drilling engineering internships while at Texas A&M. This wasn't a job that had a lot of promotion potential and I was already being paid very well so I don't have a clear progression to demonstrate. Not sure how I should convey that?

Volunteering and Leadership- I began to volunteer for translifeline a month and a half ago. I am a member of two petroleum associations but was never extremely active.
Travel- I have been to Europe several times and did some solo travel all across Europe for one month as well as solo travel in SE Asia for one month.

Uniqueness/Minority Status- I came out as transgender right after I was laid off. Transitioning is daunting and I do not know if I want to pursue it at this point in time or ever. This is certainly something that has had a major impact on my mental health throughout my life but I'm not sure if I should include it on applications if I will attend the program as male and at this point will most likely stay a male.

I feel like my overall application is fairly weak for a top ten school but I would love to attend one of those institutions.
Do I have a shot at getting into a top ten with or without a GMAT increase? I was planning on retaking the GMAT before Round 2 but I'm not sure if it matters with the weakness in my volunteering and leadership. I apologize for the word spew and thanks for the help!