The best and closest shaves I've had occur in a hot shower. I've also taken a washcloth and run it under hot water, to the point is is difficult to hold against your face. I do this several times then use the old fashion brush and soap in a cup which I've just wetted with hot water. It moistens the whiskers pretty well.
Shaving as you described, less than a day apart, require shorter and lighter strokes. I have pretty sensitive skin. Rather than do like you see in the commercial, a long sweeping motion, I use very short strokes. Apply the motion you use when trying to scrape something off, sort of back and forth, never lifting the blade from your face. It's more time consuming but seems to work well for me.
Julie