I am looking to power a 5V system at roughly 600mA from a 6V AGM lead acid battery (voltage varies from 6V-6.3V). My main concern is finding a regulator that is tolerant enough to deal with the battery at full charge down to 50% charge without too much heat being generated. A quick search on linear technology's website yielded the LT1086, but the 1.5V max dropout has given me pause since I am unsure if the the NOCO Genius G750 Charger might bring the battery voltage higher. I am mainly looking for reliability with people that don't know much about electronics, so suggestions you have on picking a regulator would be appreciated.
You need either a buck-boost switching regulator or a low-dropout regulator. The P-type output transistor of a LDO linear regulator gives a dropout measured in hundreds of millivolts versus a much higher dropout for linear regulators that use a N-type transistor instead. They are a bit more unstable though, so be sure to read the datasheet very carefully.