I reckon I’m missing something really obvious here, I thought it might work via drag-and-drop but it isn’t.
So for example, take these parameters:
What if I want to move “EXTINGUISH!” all the way to the right, how do I do that?
How do we reorder parameters?
Thank you 
If the parameters have sheets in the event, you can reorder them by dragging the tabs of those sheets around. However, if the parameters do not have sheets, there is currently no way to reorder them.
This seems like it would be a useful feature for FMOD Studio to have, so I’ll add it to our feature/improvement tracker.
@joseph Thanks for confirming!
How is the sort order of parameters determined? It wasn’t placing them in alphabetical or by creation order.
If I’m understanding you correctly: sheets can be created as a workaround to organize parameter order for usability, and have no performance or other impact aside from the manual process of creation. Right?
I’m surprised drag-and-drop parameter sorting isn’t already a thing, given its availability elsewhere in the FMOD Studio UI, so this is definitely an odd inconsistency. Including for cases where you have two closely-related parameters that you want next to each other.
Parameters with sheets are listed first, from left to right in the order of the parameter sheets’ tabs in the event. Parameters without sheets are listed to the right of those, in alphabetical order. However, if you rename a parameter while viewing an event, the order of the parameters in that event will not update until you reload the event (most commonly by deselecting and then re-selecting the event in the event editor window’s events browser).
This is correct. Sheets are purely a UI convenience to make parameters easier to visualize in FMOD Studio, and don’t actually exist from the point of view of the FMOD Engine. Adding a sheet for a parameter that is already used in the event therefore has zero effect on the event’s in-game performance.