I'm getting an annoying warbling or sitar effect on the D or fourth String only, from the open string to the fifth fret. So far, I've changed the string, tried a capo to bypass the nut and I've leveled the frets but that sitar sound persists. I've also checked for loose parts, suspecting that that one string is setting off a sympathetic vibration somewhere.

Can anyone suggest anything I've overlooked before I wrap the guitar around a utility pole?

Many thanks
Sounds like it could be at the saddle but locating the offender is key. It could be between the fret and the nut or fret to the saddle. Touch the string behind the capo as you strike the string and see if that dampens the buzz, that would be a problem with the nut. On the other side,the further up the neck you go the more angle (yes, it's microscopic)is created at the string coming off the saddle. So you get past the fifth fret and the angle increases enough to allay the buzzing. Check the groove in the saddle at that string it might be ramped. Of course, if you have to regroove that location you'll probably have to do them all or you'll have one lower string - provided there's room for lower action from the saddle.
If not, you'll have to shim or replace the saddle.