You wouldn't be spreading yourself too thin outright. You can apply to any and all military programs that you're qualified for. The real test is the administrative burden that any military application process places on the applicant. Regardless of the program, there are a lot of things to keep track of. In your case, some things have carryover like DoDMERB, the CFA, and nominations applications. HSFS is an independent program that has its own application requirements. Also, you'll most likely be dealing with recruiters and they have a lot of competition for their time. If they are Johnny on the Spot, then that makes your life easier. Sometimes, their response rate is leaves something to be desired.
That said, time management is the key. If you are so focused on your applications that your grades start to suffer, then that is a time to step back and re-evaluate.
As an aside, I wouldn't commit to anything (like joining DEP during the SA application process) before the dust settles. I'd let the recruiter know you're applying to USAFA and USNA as a courtesy (so you don't blindside them), but not much outside of that. If you do sign any enlistment papers, make sure you read them. Sometimes recruiters will be like "Hey, just sign the papers and you'll be good to go." If you want something as part of your contract (like a certain base, school, or whatever good deals the Army is advertising these days), make sure it is in there in writing. A verbal promise from a recruiter is not the same.
