Hi there,
Applying for an MBA sounds like a good choice for you. Firstly terrific gmat score, congrats!
As you know all schools will be wondering why you need an mba and what your short and long terms goals are.
As an IT consultant, also coming from a 'big name' company, you will be competing with a big pool with similar backgrounds. So you will really need to differentiate yourself not just by way of what you accomplished at Deloitte and what kinds of leadership roles you've had, but also by perhaps telling your story and what it was like as an individual moving to the US from a former soviet state. It's also not too late to start engaging in other kinds of community work/volunteering, hobbies etc to help make your profile more well rounded.
But I really love what you plan to do and is a nice segue from you already working in the public sector. It will be really intriguing to the ad coms to hear that you want to combine your passion of fitness and really making a difference in the world (through the government). It's a terrific story and speaks to why you need an mba. All schools are looking for future leaders and want people in their classrooms that really want to contribute to the well being of others. Just make sure you can give more details as to how you envision this panning out. It will also come across as authentic and a true passion since you already created an initiative/project in this field so would be important to mention that as well so they see the trend. Basically you could make a major theme in your essays/app about health, well being and fitness.
If you'd ever like to get a free assessment on your profile we'd be more than happy to chat with you. Our team is made up of former directors/managers of admissions from top business schools - including the b-schools that you are interested in so we know first hand what ad coms are looking for in terms of what to write/not write and include in your applications.
I hope that was helpful. Wishing you well.