I have driven various SFA (LR, Safari, Hilux, LC) and IFS (Nissan Tracker, Pajero, IFS Toy) 4x4 vehicles in my lifetime. It seems as if the IFS ones always had this type of "backlash" when letting out the clutch, particularly noticeable on accelerating in low range as well. It was quite alarming on an almost new IFS (newest shape) Hiluxes I drove. This same vehicle is still going strong at >100,000 km, so this seems to be an intrinsic thing with at least some IFS drivetrains and possibly nothing to worry about.
With regard to your "ping" sound from underneath, a agree it could be the nut on the gearbox end flange that loosened up a bit. Fit a new nut, torque correctly and peen. This is a common problem with SFA Hiluxes as well. The sound is often due to worn universal joints, or plain loose nuts on any of the flanges, but I see you have had those checked out already. As Bryan said, leave the flange on the diff side alone if possible.
The nut on the centre bearing is also peened, so should not work loose, but maybe worth a check as well?
1998 2.8D DC Hilux, OME, F & R lockers, 31" Hankook Dynapro's with 4.875 ratios
2011 Pajero 3.8 GLS LWB, dead standard