You may need a higher amp hour capability if you are not allowing enough time to fully recharge between starts. If, for example, you are doing multiple stops shopping at stores within a few miles of each other, then the car won't have sufficient time to recharge the battery back to the energy level lost each time you started it. The amount of time varies, depending on battery temperature as well as how low the voltage drops. It seems to me at the minimum, it needs at least 10 minutes. At the max, for normal depletion, 45 minutes. A large amp hr rating will let you do all your starts and still get you safely home. Even if you haven't given it enough time to bring the energy level back. And once you plug in and recharge from an outlet, your starter battery will be brought back to best voltage overnight with the main battery pack.
Also, how do you know the battery management system will work correctly for a LiFePo4 battery, when it was intended for a lead/acid battery? The amp and voltage charging levels might not be acceptable, and how about load leveling and balancing? That's important for lithium, but not for leadacid.
