Hotel David (very friendly place!) is well outside the ZTL, just off Piazza Ferrucci at the very beginning of Viale Michelangelo, in Oltrarno. Your closest and most convenient car rental is Maggiore-National, which is on Viale Amendola just over the bridge (Ponte San Niccolò), less than 1km away. You can very easily walk there, pick up your car and drive back to your hotel for your luggage without ever going near the ZTL. It's also a really easy drop-off location.
Borgo Ognissanti is far and complicated from Hotel David to get to. Why bother?
By the way, Magiore-National is just down the street from our favorite place for truffles, "da 'i Coco Filippo", good to know while you're staying at the David!