Project Engineer looking to break into consulting using sponsored online MBA

I graduated from a well known University (just under top 50) with a 3.7 GPA (cum laude) in Mechanical Engineering. I have been working as a project engineer in a rotational program for just over a year at United Technologies Corporation (Fortune 50) in the military and commercial aerospace and defense industry. In my two rotations thus far I’ve been doing a lot of project managemnt (budgeting, scheduling, risk management) and Six Sigma analytical work to discover and implement manufacturing process capability improvements.

I would like to break into consulting at a big time consulting firm, such as Deloitte, Cognizant, etc. Quite honestly I haven’t explored this career path that much, but right now I feel it’s the right one for me but am flexible enough if all fails. I don’t have any constraints such as a family, girlfriend, etc.

I am looking to pursue an online MBA from a top 5 Online MBA program (top 20 full time rankings) like CMU, UNC, or Indiana. With my companies coverage for further education, Indiana would be free and UNC and CMU I would have to pay for half, but may be able to get some scholarship money as well. I am not worried about getting into these programs.

My concern is whether or not it is feasible to break into the consulting field with an online MBA on top of my project management experience. I know I will not have the networking opportunities a full-time MBA would provide but I am capable of networking on my own and am willing to put in the necessary work. I just can’t find it in me to leave a Fortune 50 company to take on debt for a full-time school when instead I could gain 2-3 more years project management experience while simultaneously attaining a very cheap Online MBA from schools that have top 20-25 full-time and top 5 Online MBA programs.

Another option I could pursue instead is first getting an online MS in mechanical engineering , operations, or something else. However, I would likely need to first take time to study for the GRE. The only benefit I could see from this is being viewed as more of a technical expert in a field which could possibly help me ease into tech consulting?

Has anyone done something similar (online MBA or MS route) or does anyone have any recommendations that I should look into? I would really appreciate any advice. I feel like I’m making a huge life decision here.

Please let me know if there’s any further input you need to evaluate my situation and I can edit the post.