Keeping UIList index in sync when renaming items

Let’s say I’m listing a bunch of data in a UIList, be it a list of actions, images, or meshes…
When I double-click on one of the items and rename it, it then often changes its place in the list since lists are ordered alphabetically. This also causes the active item of the list to change since the property that holds the active item’s index (“active_propname”) is not updated (unlike when you’re left-clicking on list items).

Is there any way to update that property whenever an item is renamed, so that even when the item changes its place it remains the active item? Manually changing the index property from within the UI’s draw function doesn’t seem to be possible. What other options are there?
Or is this just a limitation of UILists in Blender?