I actually agree with Tellenbach. Rationality means reasoning from facts and evidence. Given that the Bible/Koran/[pick your book] is not sufficient evidence of God, belief in God requires a suspension of rationality. I've said it before, no intelligent argument can be made for God, because the assumption of the supernatural is totally baseless.
What you're describing is empiricism rather than rationalism, its actually radical empiricism at that, which would deny A LOT of things besides deities, divinity etc.
Scriptures are not evidence of God for anyone who does not believe in scriptural literalism, like the majority of Christians excepting the reformation/schismatic churches.
Thomas Acquinas worked out a number of proofs of God's existence from reason alone, the RCC does not hold to all of them still but it does hold that belief in God's existence is a product of reason, as well as revelation. I'm not sure that supernatural is as correct as it is to say it is mysterious.
It sounds like you're concerned to have a critical, questioning approach to your beliefs, that's great, that's a good thing and I'd recommend one of the great rationalists to you Francis Bacon, his essays on all things, including religion, are very good. He suggested that a little learning inclines people to atheism but greater depth of learning inclines the same people to theism instead.