Worn out batteries? Marine deep cycle replacements?

My Z20 doesn't have the range it did when new. My odo reads over 1000mi. I'm thinking the batteries are just worn out (or I could have a bad cell). Given how an electric bike works, wouldn't batteries designed to be discharged and recharged be better than those designed to be constantly topped off? Would deep cycle marine batteries work better than what's installed now?
Overload in CO