I can override selecting the tabs like so:
{ "keys": ["ctrl+pagedown"], "command": "prev_view" },
{ "keys": ["ctrl+pageup"], "command": "next_view" },
But how do I override moving the tabs? ctrl+shift+pageup / ctrl+shift+pagedown are not listed in Default (Linux).sublime-keymap
maybe that functionality is provided by a package and you should check the keybindings of that package
which packages do you have installed?
maybe just use https://packagecontrol.io/packages/KeybindingHelper
Maybe its a hard-coded keybinding like several ones are of that type in SM as well.
the command behind is
command: move_tab {"position": "-1"}
command: move_tab {"position": "+1"}
Maybe you are lucky with assigning some keys to that commands?