There is a script that controls this SowIncidentLandingPageUtilsSNC. One issue with it is that it is read only, so making changes directly to it is not possible.
We had a similar requirement, along with adding a bunch of other stuff. So we made a copy of it.
(Standard disclaimer: This means that you will not get all the new stuff on upgrades and you will need to review this record when upgrading to make sure you are not missing out on new features)
If you flip the order around as shown above they will switch order on the screen (see below). You can even specify the defaultSelected.
It is also possible to add additional dropdown values.
Note: Adding new choice(s), you will need to make additional changes in the script to do something with it. As you can see from the code snippet from the script below, there is an if statement that does something different based on the choice selected. You will need to look for places like this and add code to handle your new choice.
I hope this helps or gives you some ideas.
