I don't believe I have ever preached through First Timothy, but I have preached a series on the qualifications of elders (obviously looking at Titus 1 as well). I agree that a sermon per qualification might be a little much, and trying to cover them all in one sermon won't do it justice. I preached four sermons on the qualifications. That may not wrap everything up within each sermon as tidily as one might like, but it seemed to me the best way to cover the material.
καὶ ὑπὲρ πάντων ἀπέθανεν ἵνα οἱ ζῶντες μηκέτι ἑαυτοῖς ζῶσιν, ἀλλὰ τῷ ὑπὲρ αὐτῶν ἀποθανόντι καὶ ἐγερθέντι.