bl_info = {
    "name": "Set Origin to Bottom Centre",
    "description": "Adds \"Bottom Centre\" to the Set Origin's submenu.",
    "author" : "batFINGER",
    "version": (1, 0, 0),
    "location": "View3D > Object > Set Origin",
    "blender": (2, 80, 0),
    "tracker_url": "https://blender.stackexchange.com/a/182082/66364",
    "category": "Object",
}

import bpy
from bpy.props import EnumProperty
from mathutils import Vector, Matrix

def origin_to_bottom(ob, matrix=Matrix()):
    me = ob.data
    mw = ob.matrix_world
    local_verts = [matrix @ Vector(v[:]) for v in ob.bound_box]
    o = sum(local_verts, Vector()) / 8
    o.z = min(v.z for v in local_verts)
    o = matrix.inverted() @ o
    me.transform(Matrix.Translation(-o))

    mw.translation = mw @ o

def main(context, origin_type):
    for ob in context.selected_objects:
        if origin_type == 'BOTTOM_CENTRE':
            origin_to_bottom(ob)
        else:
            print(f"Add code for {origin_type}")

class SimpleOperator(bpy.types.Operator):
    """Tooltip"""
    #bl_idname = "object.simple_operator"
    bl_idname = "object.origin_set"  # override the old one
    bl_label = "Simple Object Operator"

    def items():
        items = []
        rna = bpy.ops.object.origin_set.get_rna_type()
        for i in rna.properties['type'].enum_items:
            items.append((i.identifier, i.name, i.description))
        items.append(('BOTTOM_CENTRE', "Bottom Centre", "Set origin to Bottom Centre"))
        return items

    type : EnumProperty(items=items(), default='GEOMETRY_ORIGIN')

    @classmethod
    def poll(cls, context):
        return context.active_object is not None

    def execute(self, context):
        main(context, self.type)
        return {'FINISHED'}

def draw_menu(self, context):
    self.layout.operator_menu_enum("object.simple_operator", "type")

def register():
    #bpy.types.VIEW3D_MT_object.prepend(draw_menu)
    bpy.utils.register_class(SimpleOperator)

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