Fretless bass - nut slot height

[Random Guitarist]

Hi, hoping for advice for the nut on on my fretless. 

 

It's  a frankenbass with Squier body and a mighty mite neck I bought used. The neck was five string but has had a tuner removed and a replacement four string nut fitted. The problem I'm finding is intonation relative to he open strings is off (sharp), especially it's noticeable near the nut. 12th 'fret' intonation is OK but I had to move the saddles back a lot to make it so. I know I can move my fingers to compensate, but the in tune positions just 

 

I'm thinking I can maybe fix this by lowering the nut slot. It seems to me that, on a fretless neck, the nut should be slotted very low almost down to the fingerboard. Is that right or should there be a significant gap between the bottom of the string and the fingerboard at the nut?

 

Thanks, Grant 

[Velarian]

I recently had a new nut fitted to my fretless Precision by a luthier and although it’s low there is still a gap. A rough and ready check tells me it’s less than the thickness of credit card. I can check it more closely with feeler gauges when I have time later if necessary. 

[Random Guitarist]

Thanks, definitely a bigger gap for me than that, time to try some filing . . .

 

[Random Guitarist]

I figured it out, the reason I was finding such an issue was that The E and A had high nou slots and the d and G has sensible ones. I saw this when I looked more closely. Now I have lowered the offenders my finger positions are consistent across the strings and intonation is a lot less weird.