Many people have shared their thoughts on this issue for the past 5 decades. Personally, I have reviewed over 50,000 resumes, from all over the world, in the past 22 years. In that time, I was continually struck by the typical reaction from a civilian - towards a military CV. Generally, confusion.
I'll remain brief with my recommendations:
Do not mask a gap in your resume. > These big companies are already making you a priority for hiring. However, if they weren't trying to filter you out, your interview would begin with an offer letter, right? Don't give them any reason to think you are trying to hide or mislead. If you have a gap in your resume, OWN it; turn the tables on it. Getting a job IS a job. You have been interviewing companies too, right? You've been selective and looking for a great team to commit to, right? Of course!
Group your MOS codes / skills / rank / etc. > Hiring managers will be thrown-off by having these all over your resume. They know you are a transitioning Vet anyway, don't distract them by muddying-up the resume.
Do not pay someone to write your resume. > This will backfire and it will be a waste of money. You need to speak to how YOU wrote it and the hiring manager will be able to tell if you didn't. Other Vets have gotten a job with their resume, format yours like their's.