You really might want to invest in either getting a buck-boost voltage regulator or some sort of an (possible illegal. Al is the guru here) isolated capacitor bank to feed the reg when the voltage drops under 7.2 momentarily.
I, myself, would use a secondary "bridge converter". They is rated for 5v@1A, so it will directly work with your design. You also get the bonus that they have gone through quite rigorous testing in FRC, because every team uses one to power their communications. This would probably be your best bet if your team has any spare converters laying around!
I power our team ODROID using a bridge converter. The voltage is quite stable and barely dropped bellow 4.98v and went over 5.03v when I tested it with a battery connected directly!