You can already manipulate the order very easily with some lines of CSS since we use the flex property.
E.g.:
-
Default order

-
Custom order

CSS example:
.custom-header-links li {
&:nth-child(1) {
order: 3;
background: red;
}
&:nth-child(2) {
order: 1;
background: green;
}
&:nth-child(3) {
order: 2;
background: yellow;
}
}