I've put some time into playing this sans pickups just to try to get back into it.
Now it's had some time to settle, the annoying noises are starting.
I think the big one is replacing the nut - the original on there is done for, and the strings are deep.
Both E's are problematic. The 6th is hitting the first fret open and making a lot of noise.
The 1st is problematic on the second fret. If I fret the 1st fret, I'm hitting the second and coming out with a dead note. The string is cut well into the nut so I'm thinking that perhaps it's just too low. I don't want to jack the string up at the bridge and blow the action out to get around it. 2nd string is better, but it's on the edge of hitting it.
I thought for a second it might have been the new fret, but then I remembered that it's been a bug bear for this guitar for years.

I've ordered a couple of cheap synthetic nuts to have a crack at. Not entirely sure how I might go about remove the old nut yet, so that should give me something to look into this weekend.