When I promote someone along the track, the players nametag above the player and in the tablist doesn't get updated until I use /nte reload. This worked fine with PermissionsEX. Are you able to make this compatible?

This must be done by the developers of NametagEdit.

Also that is why I made my own plugin to replace NametagEdit fully: https://github.com/StoneMain/Shortranks

This plugin isn't available on spigot?

No, but you can download jar from Releases tab

Edit: I am avoiding SpigotMC for personal reasons.

Looks like someone has already pull requested the functionality.
sgtcaze/NametagEdit#161

It’s a shame to see things like that being rejected for the sakes of maintaining compatibility with ancient Java versions. Software has to move on at some point.

I suggest you find a different plugin to use. @mikroskeem ‘s project looks like a great alternative. :)

It doesn't seem to be a full replacement of NameTagEdit sadly.
And as far as I know there isn't any good alternative available on Spigot.
I guess the other way around isn't an option?

Define full replacement. I may implement things you'd like to have. Feel free to ask questions on Shortranks issue tracker.