I'm sorry you haven't received a reply but it is just the same day. I'm also waiting on a reply so I'll write to you. I have only one property that I rent out and do it myself so I am learning with each turn over.
It is supposed to be first come first serve but you are right,I think that a little delay by either landlord or applicant for different reasons can mean the difference in who gets in.
Ask for an application prior to viewing and have it ready to go when you get there. If you know you want it before viewing, ask if it is possible to apply early.
First of all, fill out and answer all questions completely and quickly. Inquire every other day about progress so they have a harder time brushing you off? Ask when they will come to a decision.
Your credit score is good and you say strong income. Specifically, you need to make 3-4 times the rent which is the major criteria. Knowing that you are not staying more than two years might be a turnoff as you know it takes a lot of work and money to get unit re-rented to qualified applicant. Don't volunteer the two year information if they don't ask. It's a military area so they are probably used to applicants that may leave in a hurry and may have ways to account for that. Perhaps offer to pay a bit more for a short stay, offer two year lease, or ask for month to month lease for a bit more?
I don't think it's a turnoff that you have a rental. It is an asset that you know what it's like on the other side and will likely be more respectful of property and terms of lease.