Hi and thanks for your interesting question. I have learned something new!

I have not heard of the letter of support from Employer. The only letters of support I am aware of is Alums sending them in behalf of the applicants during the waitlist situations. This must be an Asia provision. Is this in addition to the letter of recommendation or instead?
My experience with EMBA admissions however is that they are very open and very welcoming to qualified candidates and would not reject anyone without giving it multiple considerations.
What is your plan? It sounds there is some leave required from the job, what is your plan for taking that time off? Use vacation? I think the program is mostly concerned about you not over-estimating your ability to take time off and not stretching yourself too thin. If you have a plan how to address it, I would discuss it with the EMBA AdCom. They won't ding you for talking to them and instead would be welcoming of anyone approaching them and will be happy to work it out. (EMBA admissions are very different from FT/PT programs; EMBA is for-profit, so it is a business opportunity for them to have you as a student). You can first tell them about your challenge, how you are planning to tackle it and if that would work and perhaps about what is the purpose of the employer support letter....
BB