First and foremost, I'd like to encourage you to seek God's voice in whatever way you usually hear him. Some hear the still small voice, some see flashing neon lights, some receive God's guidance through the words of others, I personally feel God in "the peace". I have never had a strong tangible sense of God telling me to do something, rather I feel at peace with a certain decision (when I let myself calm down), and that's consistently the way God directs me.
So first and foremost, "listen" for the way he directs you. Then don't be afraid to follow it.
Brief story: Shortly before I got married, I was second guessing a lot of things. I got all heady about getting married, and demanded some sort of sign from God. I said "peace isn't enough, this is marriage!" and I begged and begged for some kind of big booming voice to direct me. What I got instead was at least 2 different people praying with me at different times saying "I really feel like God's guiding you through his peace. Follow the peace in your heart." So... I've learned my lesson.
As for practical advice, I think you really need to search for God's heart in this. The opportunity at NASA sounds awesome, but if God's put it on your heart to focus on your relationship with Him (at the expense of music), then the outcome of that will be immeasurably better than any worldly job offer. I generally don't believe God "tests us" in the way many people say (I'm going through tough times, why is God
testing me?) but I do believe God wants to see your obedience.
Regarding getting into the Grad program. Don't forget God can make a way in any situation. Don't use that as an excuse to slack off, but don't forget that God has infinite resources and desires to see his children succeed and live out their dreams.
And, if you don't get into the Grad program but opportunities continue to open at NASA, who needs the grad program? I don't know if your industry is like mine, but I think much of the North American work force has shifted over the last couple of years to looking at experience rather than education.
Is all this advise conflicting and contradictory? Sure. Basically, don't forget that God can count you into and out of any situation. Don't rely on your own strength

And first and foremost, spend time with him, and "listen", expecting to "hear" something.