Often it's wiser to repair a blown slot than it is to replace the whole nut. But allow us to have an understanding: I ordinarily leave a nut slot a little higher than necessary at first, to allow for the string to cut itself a little lower. This is a classic case of apples and oranges.
Here's a shimmed-up mess of a nut that has all the problems: Trim and dress the nut as if it was new and uncut, then cut the new slot. It's about friction in the slot.
I prefer to shape my slots in the shape of a horn's bell: I have to say I am impressed. I appreciate and admire fine scale detail and prefer my slot cars to mimic the 1: It roulette point blank isn't going to impress them. This assumes the frets are really true and level. Avoiding hitting the first fret, assuming there is one, I cut down below the blown slot, sometimes almost to the board itself, angling the saw back a bit.
If it's too flat some repair books actually advocate this! Whether the string is coming from the top or the bottom of the string post, it will slide smoothly into the nut slot. There are many facets to our hobby today and depending on your own personal involvement will decide just how important this release is.
Make sure the wheels and spur are tight and that they front axle is not binding. Lack of printed instructions would be fine if they were available online but the website for Thunder Slot is not completed as it's a simple page under construction.
It leaves a nice flat-bottomed slot. Here is a quick photo of the two cars side by side just in case you are curious.
The precise shape of the slot at the front edge is extremely important for sound quality, stability of the setup, and intonation.