Trouble getting the right cup and cone hub adjustment I have a pair of Shimano XT wheels and recently had issues with the hub on the rear wheel requiring new cones and bearings. These were fitted carefully but I've had issues getting the right adjustment tightening the cones.

On the one hand I can tighten it to a point which effectively prohibits rotation, and there is no play. But to get the hub to anything close to a smooth rotation I get a tiny amount of play. I have experimented extensively and cannot find any way to balance not having any play with having smooth rotation - in context smooth means turning cleanly, I realise there may be some friction, particularly with new parts. Conversely when I loosen so there is just a hint of movement I get very smooth rotation.

I've been testing with very small increments in tightness - probably around 3 degrees at a time.

The only thing I can think of is that I've used a general purpose grease rather than a hub bearing specific one, but I would expect that to be a difference between degrees of smoothness, rather than the difference between working and not working.

Can anyone provide any tips or suggestions as to how to address this?

Many thanks
Getting the adjustment right is sometimes difficult and is as much art as science.   I rebuild lots of old bikes, and frequently have to rebuild wheels. Here's what I do...

First, be sure to work from one side.  Normally the non-drivetrain side; that way your axle will stay centered.  Clean everything up and inspect carefully.   Since you've already bought new cones... Should be no problem.
The difficulty, as you note, is making the final adjustment.  You can get everything all set up so that it's apparently perfect.   Then you apply the cone wrench to hold everything in place and tighten the locknut....And it's too tight.
The problem is that the axle itself will tend to move when you tighten the locknut.  So...When I get everything set to tighten down, I then clamp a big pair of vise-grips on the other side of the wheel, and hold the thing in my lap so that the vise-grips are held in place by my knee.
Then, you can hold the cone in place and tighten the locknut with little chance of the axle moving.
As to the exact adjustment.... It's always been the paradigm that if you have QR skewers, you leave the adjustment so that there's just a tiny, barely perceptible amount of play so that when the skewers are tightened they take up that slack.
I've never done it.  I always set mine so that the axle rotates freely and there is no perceptible play.  I also don't tighten my skewers nearly as tight as all the "industry" guys recommend.  Don't think it's necessary.