LMC6062 Jumps too Rail when 1V below
Look at the datasheets!

The LMC6062 datasheet says on page 3:

Input common mode voltage range: \$0..V^+\$ − 2.5V 

i.e. at \$V^+ - 1V\$ you are already 1.5V above the range that is guaranteed to work.

The LMC6482 datasheet on the other hand says it is a rail-to-rail input and output OpAmp, i.e. it works with input voltages from GND rail (0V) to up to the \$V^+\$ rail.