depending on year, you are allowed to fail a certain amount of emission monitors. Enough of the monitors must be set to pass plug in. if they are not set, it doesn't necessarily cause a CEL. My ZJ has 6 i believe.
you driving around at greater than 1/2 tank just means the jeep has not run the emissions test yet.
id suspect gross evap leak will be the code. check hoses on canister system, gas cap, ect.
unplugging the battery hurts you here as all the monitors are reset and need to re perform the tests and self pass.