A few other options for you:
A: Get a Guarantor - a person who is willing to guarantee your rent payment if you can't pay -- like a co-signer on a car loan . Your Guarantor will need to submit employment and income info to the landlord as well.
B: Get a lease guaranty insurance policy. (For Example: Insurent.com). The Lease Guaranty Insurance takes the place of a human Guarantor. It is an insurance policy that will pay the rent to your landlord if you do not. The prices on these policies can be high as they are also based on risk -- but if you have $13K+ in cash to work with, it may be an option for you if you can't find a landlord who will accept you with 6 months pre-paid rent.
C: Look for a 6 month lease (with option to renew). Since you have 6months worth of rent -- try for a 6-month lease and pay it all upfront. Then there is very little risk to the landlord. That would give you 6months of time to change your employment status and/or accumulate another 6 months worth of rent to renew and pre-pay again.
So, yes pre-paying 6 months of rent will help your chances - but depends on the landlord. As I've noted, there are other ways to leverage your cash on hand. Just be creative and you can make it work.
Best of luck ... and thank you for your service. Very much appreciated.
While it may not be necessary, you should definitely increase your chances by being able to offer 6 months up front.
I would also have all of your paperwork ready - showing that this is part of your income. any landlord is going to want to see proof of income, last years tax returns, and bank statements at the very least, so you may as well be up front with them from the very beginning.
Best of Luck,