That's kind of a strawman. Serious Catholic thought (John of the Cross, Teresa of Avila, Pope Benedict, etc) doesn't try to "remove the doubt" at all. I highly recommend Ratzinger / Benedict for modern text, and the great contemplatives for non-modern texts. They grapple with doubt and all other tricky subjects head on, and have a broad (and in my opinion accurate and subtle) view of the journey of life.
I was also going to recommend John of the Cross. There's also a whole tradition of apophatic (negative) theology, and an associated tradition of darkness mysticism (e.g. Pseudo-Dionysius). That your doubts are founded in the reality that God is unknowable-as-such, and even "existence" may be an invalid concept to apply to the divine.
In that vein, but I've been reading a book that synthesizes John and Teresa and the gospels. It had a few gems that stood out to me recently. On the importance of voiding oneself of all: "He is not only beyond all things, but boundlessly beyond them. Created realities are... more unlike God than like Him.... However impressive may be one's knowledge or feeling of God, that knowledge or feeling will have no resemblance to God and amount to very little."
