That's very high. Definitely needs to be lower. It's the height over the 1st fret that matters and should certainly be less than 0.5mm, StewMac reckon on a clearance of about 0.15mm to 0.38mm from top E to bottom E. But you really need to check with all the strings on and up to tension. You can use feeler gauges to guide you.
But with that much slot to cut, I'd suggest filing the bottom of the nut first to take nearly 1.5mm off, then use the files to lower the slot depth from there, as they look pretty lightweight in the photo and look more suitable for fine work. But do the slot filing in-situ with the neck strung up and just the string on the slot in question loosened and pushed to one side. The string tension will pull the neck upwards, so if you try and slot it with no tension you'll end up with a bigger gap than necessary.
If done correctly, then you should hardly use any finger pressure to fret a string at the first fret. Obviously, loo low and you'll get buzzing, so it's a fine line.
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