You said you already have a new driveshaft installed- which driveshaft? Unless you did both, it could be the u-joints in the one you didn't replace. The front shaft is pretty much right under your seat, and could sound like the middle of the vehicle.
My experience with axle/driveline noise on other vehicles/jeeps is that CVs, unless totally destroyed, make the most noise when turning, or at least have a change when turning. You say nothing changes when turning, so I want to rule out the CVs.
Diff bearings and wheel bearings usually make different noises depending on acceleration or deceleration, or high load, coasting, cruising, turning (side load), etc. However, my experience with these issues was on solid axles, but i would assume the concept is the same. While I've yet to hear about diff issues specifically with the XKs here (unless offroaded really hard), that doesn't mean it can't happen. Also, these noises are more "whirring" or "growling", not really any clicking or clunking unless you have a broken tooth in the diff....which, i seriously doubt you have.
I had a front wheel bearing go out in one of my old XJs that sounds like what you're describing, but that was a solid axle with (i think) a type of ball bearing, so completely different than ours. It was very obvious where from exactly when i was driving with the windows down next to a wall or large, flat surface; like a concrete bridge barrier or highway divider.
Check out this page with descriptions of diff and driveline noises, pretty accurate: Diagnosing Differential Noise