Upload & Sell: Off
Ok, LENR is definitely off.
Very odd that it only shows up in exposures longer than 30 seconds. Try some more tests to be certain of that, like the same scene with 40 sec, 30 second, and 20 second exposures in that order.
The reason for trying a frozen gel pack is because the camera generates heat during long exposures.
You may have to send it back, but most cameras sent back are in perfectly good working condition. Yours might have a genuine flaw that you are lucky you noticed soon, since it concerns you.
Some Raw conversion software can map out hot/dead pixels. You are shooting Raw, right?