I'd also suggest buying and fitting a string retaining bar for the headstock. Obviously you'll need a 7-string version. This fits behind the nut and should be set low enough to pull the headstock end of the strings flat across the nut itself as shown in the picture. They only cost a few $ and are easily found on eBay.
This lets the string clamps work 100% on keeping the string from moving, rather than also having to try and press the strings down onto the nut at the headstock end, which is never as effective at stopping string movement.
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