"Выедет" подразумевает некоторое ожидание, а "выезжает" это сию минуту,(он уже выезжает) уже в действии

"Сейчас" in Russian is not only used with present, but with future tense also. Think of it that way. "сейчас+глагол в будущем времени" is an equivalent of Enlgish Present Continuous tense. When you say, for example: "He's going to fall now". Here, although in English you use a kind of present tense, you actually talk about a near future. In Russian, you we say the same like this: "Он сейчас упадет". If I said "Он сейчас падает" it would mean that "He is falling RIGHT NOW", in this exact moment he is in the process of falling. So, "сейчас+глагол в будущем времени" means that this something is going to happen in the next moment.

В вашем тексте правильно -выедет.