Addon: how to update filename on EnumProperty change?

Question

I'm working on a Blender (2.93) addon that outputs models to a few different formats. There is an EnumProperty in the filebrowser which lets the user choose which format to output to. The formats are different enough that I feel they should each have their own filename extension, but I cannot figure out how to do this properly.

This is the code I'm using for exports, with some of the irrelevant properties trimmed out:

class ExportData(Operator, ExportHelper):
    bl_idname = "export.gtd"
    bl_label = "Export"
filename_ext = ".buf"

def update_ext(self, context):
    new_ext = ".buf"
    if self.output_type == 'vertex_buffer':
        new_ext = "buf"
    else:
        new_ext = "gml"
    params = context.space_data.params
    context.space_data.params.filename = f"{Path(self.filepath).stem}.{new_ext}"

filter_glob: StringProperty(
    default="*.buf;*.gtd",
    options={'HIDDEN'},
    maxlen=255,
)

output_type: EnumProperty(
    name = "Output Type",
    description="The type of data to output",
    items = (
        ('vertex_buffer', "Vertex Buffer", "A vertex buffer that can be loaded at runtime"),
        ('debug', "GTD Script (debug)", "A human-readable script that can be used to import and debug"),
    ),
    default = 'vertex_buffer',
    update = update_ext,
)

def execute(self, context):
    return export_gtd(context, self.filepath, self.output_type)

When I run this code, I can use the console to verify that the filename_ext changes, and it will print the correct filename if I print context.space_data.params.filename. There are two problems, however:

• The filename_ext variable always forces a single filename extension on the output, and I can't figure out how to change it.
• The actual filename at the bottom of the filebrowser doesn't update when I change the choice in the EnumProperty.

I've been studying this answer: Addon: how to make Blender run check()/redraw when option changed?, but the suggestions/solutions there don't seem to work. Would appreciate any help pointing me in the right direction on this!