Any suggestions?
A possible candidate might be a Fluke 27? Dave did a review/teardown
It is easy to use, sealed very well (as shown in Dave's video), has min/max and easily found on ebay for under $100 (Dave got his for $40).
It doesn't have backlight or use AA batteries, but the Fluke 27 will run 1000 (one thousand) hours on a 9V battery.
From
http://www.fluke.com/fluke/caen/digital-multimeters/Fluke-27.htm?PID=56055Extremely Rugged, Water Resistant, O-Ring Sealed for Harsh Environments
The Fluke 27 combines accurate digital and analog measurement capability with extreme ruggedness and durability. They have cases twice as thick as any other DMM we build. They are totally sealed, waterproof to 3 feet (one meter) of water for one hour, tough enough to withstand contaminants, chemicals, accidental drops and severe electrical overloads.
Designed to meet military specification of MIL-STD-28800 for Style A, Class 2 instruments, the Fluke 27 performs under the extremes of heat, cold, humidity, shock, electromagnetic interference, vibration and downright abuse.