Seconding this - I've done the month overlap thing twice, with cars and a moving truck and everything. Once because my current landlords expected me out on the last day and the new people wouldn't let me move in until noon on the first even though the place was already empty for "renovations" (slapping another coat of white paint over everything, dirt and all). The other time because I had a line on a great place and didn't want to miss it. It still made moving way easier and I was able to skip the moving truck that time.