Some good reading and sensible information at http://www.windsun.com/Batteries/Battery_FAQ.htm
11.9 will be the open circuit voltage. Dip on load can be considered as a transient effect and is a function of internal resistance which is principally indicative of battery capability (capacity) rather than depth of discharge. (As a battery ages, through use, its fully charged capacity reduces and its internal resistance rises)Certainly a battery half charged will show a greater dip than one fully charged but it is the overall condition, rather than state of charge, which governs internal resistance.
Use a mosfet? Then its not a physical connection to go back after arcing a million times, and no click noise