Thanks for this information. I've already got the relief and action to where it should be, as I've been playing her quite a while. I didn't know about the nut situation or about pressing the strings down, though that makes sense. Why are the nuts cut like you say?
Cutting a nut correctly is a time consuming, painstaking process. And at the end it comes down to make a few passes with a the file, restringing to pitch, checking it, and repeating. Now if you go too far with a file, then you have to start all over again. That's why most factory nuts are cut too high. Leave it a little high and you won't run the risk of having to start over again, so they can get the product shipped sooner.
Read the sticky threads at the top of this forum for instructions on set-up, and see if it's something you want to tackle. I tweak the nuts on instruments I buy (haven't had to do it on my three fretted Laklands, nor two of my three Guild guitars), and have for about 20 years. It's not really hard, but you have to be patient and plan on a few "do overs" when you're starting to learn this.
In addition, there is no way to get a fretted instrument to play exactly in tune all over the neck. But there are some things you can do to help alleviate the problems, besides the tips in this thread.
Make sure you use a really accurate tuner. Now, that means to me, a Peterson. No matter what name is on most tuners, they use the same quartz timing device and have pretty much the same accuracy. The difference between ± 1 cent (the Boss TU-3 for example, but most tuners are in this range) and the ±1/10 cent of the Peterson is probably meaningless for getting your bass in tune at a gig. But, when setting the intonation, it can become critical. If your open string is flat by 1 cent and your fretted note is sharp by 1 cent, your typical tuner will tell you they're the same note, but you're off by 2% of a half-step. The more accurate tuner will only allow you to be off by 1/10 of a cent either way. So, start with a good tuner.
Then, hold the bass in playing position while doing the intonation. The weight of the headstock can move the neck enough to throw things off.
I also pluck the notes about once every second and read the attack of the note rather than the sustain. That's what you hear when you play mostly, so use that.
Then if it's really exasperating, try this trick (I learned this from a Johnny Smith- the reknowned jazz guitarist from the '50s and '60's- in a Guitar Player Magazine article on set-up back in the '80s). Compare the fretted note and the harmonic at the 17th frets. To get some instruments to play acceptably in tune across the neck, I've had to average the results of the 12th and 17th frets to come to a compromise.
And finally, don't be afraid to tweak the intonation so it works for where YOU play. If you don't go past the 7th fret much, then adjust things so the bass plays in tune in the lower registers and don't worry that it's a little out up at the 15th fret.
Hope this helps!
John