I haven't found a way to cut it off but if you hold the key fob up to the frame between the door handle and the frame when you close it, it will not beep.
I went to test drive a 21 JTRD today. I have been debating what to do. I sold my JTR last year and I miss it but the 3.6 just wasn't a good fit in my opinion.
I have been looking for a Gladiator diesel. I talked to a dealer today that said they had 8 diesel Gladiators & Wranglers in the back they couldn't sell. They have to sit on them until the stop sale is lifted. Said it could be weeks or months.