Had the same thing with my JTL kit. You need to shim the headstock end of the pocket until the strings aren’t touching.

Then use some feeler gauges to measure how thick the gap is from the shim. Write that measurement down.

Remove the neck and measure the thickness of the neck at the heel with some digital calipers (both bass side and treble side) Write these measurements down too.

Now with the neck clamped on your bench with the screw holes facing up, You need to use a hard sanding block (very important) with some 80grit to sand the body end of the neck heel. You want to take off the thickness you measured with the feeler gauge at the start. I sanded to about halfway between the 4 screw holes on mine.
Keep stopping and checking with the digital calipers to make sure you’re sanding it evenly.

Long story short: if the shim needed to be 2mm and your neck heel is 60mm, you need to sand it to 58mm.