2001 3.0L V6 automatic gearbox issue

[Archangel]

My beloved S Type started severe juddering between 1500 and 2000 revs when going up a slight incline. It feels like the gearbox wants to change down but doesn't quite make it or it cannot make up it's mind. I either have to kick down or drop a gear manually. I had the transmission fluid changed and was told that the old fluid was smelling burnt.  The problem continued and I had the fluid changed again, in case there was any previous residue - but still no improvement. I'm no mechanic, but am wondering if there is any sensor, manual or electrical, that could be the problem? I am trying to avoid a gearbox strip down if there are any obvious causes that won't necessitate this.  Any suggestions welcome.