Profile Evaluation Request- Any chance to Tier-1 EU MBA programs?

Hello MBA Coach,

I am decided to start application for an MBA (preferably in Europe). My prospects are IMD, HEC and IE for 2023 intake, but I also considering Mannheim or WHU for 2022 intake ). Some college buddy who is a recent graduate from LBS told me that if I retake the GMAT with a 760 and put all my efforts in a wise application, I could have some possibilities with INSEAD and LBS (However, I am not very convinced with the idea to wait for 2023- Aug/Sep intake) ..Do you think it is a good idea?

Please kindly check my profile and give me some feedback.

Background and nationality:
31 years old male, Peruvian, with 5 years of work experience in engineering and business development.
Undergrad Information:
BS Mechanical Engineering from National University of Engineering of Peru- GPA: 3.0
BS Industrial Engineering from National University of Engineering of Peru- GPA > 3.5 (1st place in the class)

GMAT:
720 (Q-51 V-36 IR-8 AWA-4)

Work experience and leadership:
-Asset Maintenance Trainee in a hands-on experience internship at field operations for an International Oil Company – 01 year
-Assistant for an independent consultant on management and processes – 1.5 years (while studying my second major)
-Product Specialist for a small B2B company that sales machinery – 6 months (transition to commercial area)
-Business Development Analyst in a global company (machinery manufacturer)- 02 years //Currently
-Indirect Sales Responsible as an acting role in the same company listed above – 01 year //Currently
-Entrepreneur with an e-commerce startup founded by me and a group of friends – 01 year //Currently

Regarding leadership experience, I have not yet held a job position with some staff in charge or a middle-management position. I struggled with the process of career turning from engineering to commercial management (I stopped to work for a whole year to take the junior classes of my second major). However, as I am doing well in my current job position, they gave the opportunity to lead the strategy implementation of indirect sales which includes to plan, start and monitoring relationships with business partners and distributors. Also, as CEO of my own startup, I have to lead a team of 04 people and drive the company to a next level (Although is a small company, I am learning many valuable lessons of leadership)

Community:
- 05 years of volunteer in TECHO, an NGO that focus on poverty alleviation in Latam.
- Leader of many projects launched by TECHO for the construction of emergency houses in poor urban communities in Peru.
- Member of the TECHO’s delegation for humanitarian aid during the national emergency caused by natural disaster called “Fenomeno del Niño” (2017).
- Leader of the team of digitalization of data of poor urban communities to help people in need during the pandemic caused by Covid-19 (2020)

International exposure
I have not worked or studied abroad. However, because I work for a global corporation, I usually coordinate with people from different nationalities.

Post MBA goals:
1) Joining a global corporation as a leading role in business development, strategy, or marketing. It could be a company in the same industry of my current company (machinery) but I am open to explore another industries such as tech or e-commerce.
2) Joining a startup or founding mine (This is something I have been considering during the last year as a result of my entrepreneur experience)