How do I add a Specials Menu to the Video Sequencer?

Question

There doesn't seem to be a context-sensitive "Specials" menu for the Sequencer(like shortcut key 'w' in 3d View). How do I add one to the Sequencer with python scripting?

(I know about the "Add" menu in the sequencer, and options can be added to this one, but I need a new menu only containing context-sensitive editing options. Ex. if there is a gap between two strips at the mouse cursor position, then a "Remove gap" option would become selectable in the menu.)

This is where I am at the moment(menu containing the add menu options):

import bpy
from bpy.types import Menu

class SEQUENCER_MT_edit(Menu):
    bl_label = "Edit"
    bl_idname = "sequencer.edit_menu"                        # ID name of the class that code will call, lowercase
    def draw(self, context):
        layout = self.layout

        layout.operator_context = 'INVOKE_REGION_WIN'

        layout.operator("sequencer.movie_strip_add", text="Movie") # Example options
        layout.operator("sequencer.image_strip_add", text="Image")
        layout.operator("sequencer.sound_strip_add", text="Sound")

        layout.menu("SEQUENCER_MT_add_effect")

addon_keymaps = []
def register():
    bpy.utils.register_class(SEQUENCER_MT_edit)

    # handle the keymap
    wm = bpy.context.window_manager
    kc = wm.keyconfigs.addon
    if kc:
        km = wm.keyconfigs.addon.keymaps.new(name='Sequencer', space_type='SEQUENCE_EDITOR')
        km = wm.keyconfigs.addon.keymaps.new(name='3D View', space_type='VIEW_3D')
        kmi = km.keymap_items.new(SEQUENCER_MT_edit.bl_idname, type='RIGHTMOUSE', value='PRESS', shift=True)
        addon_keymaps.append((km, kmi))

def unregister():

    for km, kmi in addon_keymaps:
        km.keymap_items.remove(kmi)
    addon_keymaps.clear()

    bpy.utils.unregister_class(SEQUENCER_MT_edit)


if __name__ == "__main__":
    register()

Answer 1

This seems to be working, however, the cut functions aren't called properly for some reason?

import bpy

class SequencerEditMenu(bpy.types.Menu):
    bl_label = "Specials"
    bl_idname = "SEQUENCER_OT_sequencer_edit_menu"

    def draw(self, context):

        if context.space_data.type == 'SEQUENCE_EDITOR':

            layout = self.layout
            layout.operator("sequencer.gap_remove").all = False
            layout.operator("sequencer.gap_insert")
            layout.separator()
            props = layout.operator("sequencer.strip_jump", text="Jump to Previous Strip")
            props.next = False
            props.center = False
            props = layout.operator("sequencer.strip_jump", text="Jump to Next Strip")
            props.next = True
            props.center = False            
            layout.separator()            
            layout.operator("transform.transform", text="Grab/Move").mode = 'TRANSLATION'
            layout.operator("transform.transform", text="Grab/Extend from Frame").mode = 'TIME_EXTEND'
            layout.operator("sequencer.slip", text="Slip Strip Contents")            
            layout.separator()
            layout.operator("sequencer.cut", text="Cut (Hard) at frame").type = 'HARD'
            layout.operator("sequencer.cut", text="Cut (Soft) at frame").type = 'SOFT'           

addon_keymaps = []
def register():
    bpy.utils.register_class(SequencerEditMenu)

    # handle the keymap
    wm = bpy.context.window_manager
    kc = wm.keyconfigs.addon
    if kc:    
        km = wm.keyconfigs.addon.keymaps.new(name='Sequencer', space_type='SEQUENCE_EDITOR')
        kmi = km.keymap_items.new('wm.call_menu', 'W', 'PRESS')
        kmi.properties.name = "SEQUENCER_OT_sequencer_edit_menu"    
        addon_keymaps.append((km, kmi))

def unregister():
    bpy.utils.unregister_class(SequencerEditMenu)

    for km, kmi in addon_keymaps:
        km.keymap_items.remove(kmi)
    addon_keymaps.clear()

if __name__ == "__main__":
    register()