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"How does one choose a Doctoral program in this case?"
One chooses in this case the same as in every other: by seeking God's direction through prayer, and perhaps fasting, and through study of God's Word.
No one here can give a proper answer as to what you should do. We might suggest schools we know about and have liked, but even these suggestions could never hope to take the place of knowing what God wants for you to do.
The Bible is filled with examples of people asking God what to do--and they each found His will for them in varying and unique ways. For some, God may give a vision or dream, like in the case of Joseph who was told to go ahead and marry Mary, and later, to take her and the babe to Egypt. For some, God may give a physical sign or symbol, like in the case of Gideon's wet or dry fleece. For some, God will send an angel to bar the way, as happened to Balaam (who afterward stubbornly pushed for his own way anyhow). For some, they may hear a whispering in the trees, as did David (see 2 Samuel 5:24).
James 1:5 gives us a promise that we can claim when seeking God's guidance.
If any of you lack wisdom, let him ask of God, that giveth to all men liberally, and upbraideth not; and it shall be given him. (James 1:5, KJV)
But this verse is followed up with "But let him ask in faith, nothing wavering." (vs. 6). When we ask according to His will, God is happy to lead us.
The steps of a good man are ordered by the LORD: and he delighteth in his way. (Psalm 37:23, KJV)
And thine ears shall hear a word behind thee, saying, This is the way, walk ye in it, when ye turn to the right hand, and when ye turn to the left. (Isaiah 30:21, KJV)
I will instruct thee and teach thee in the way which thou shalt go: I will guide thee with mine eye. (Psalm 32:8, KJV)
Sometimes God's guidance comes in the form of finances. Sometimes applications are accepted or rejected, perhaps seemingly without justification. Sometimes people may say things suggesting God's will for us--perhaps without realizing that they are doing so. Sometimes we read something from the Bible, or God gives us an impression, that seems to point out our duty in bold print. It is our place to pray in faith, then to move forward, then to accept the outcome as God's will, whether we may be at first pleased or not. We cannot, however, expect for things to just happen while we sit idly by. We must do our part to help answer our own prayers, for faith without works is dead (see James 2:17).
Those who truly seek God will find that their desires are given them of God, and God will, with the desire, make a way for its fulfillment.
Delight thyself also in the LORD: and he shall give thee the desires of thine heart. Commit thy way unto the LORD; trust also in him; and he shall bring it to pass. (Psalm 37:4-5, KJV)
Request, trust, and accept God's guidance, in faith.