python+kivyでボタンからの再帰処理（定周期）停止

Question

Python + kivy でGUIデスクトップアプリを作成しています。

下記のコードで実行したところ、「Run」ボタンを押した後、画面が触れなくなり固まってしまいます。
「Run」ボタンで再帰処理を実行、「Stop」ボタンで停止がやりたいことです。
threadingを使ってマルチスレッドで処理しようとしている所のがまずいのかなと思うのですが、解決策が浮かびません。

---

import japanize_kivy
import webbrowser
import time
import threading

from kivy.app import App
from kivy.uix.widget import Widget
from kivy.uix.floatlayout import FloatLayout

from kivy.properties import StringProperty
from kivy.properties import NumericProperty

from kivy.core.text import LabelBase, DEFAULT_FONT
from kivy.resources import resource_add_path
from kivy.clock import Clock


class MainScreen(Widget):
    site_url = StringProperty()
    count = NumericProperty(0)
    text  = StringProperty()
    interval_time = NumericProperty(0)
    run_flg = True

    def SiteAccess(self):
        #webbrowser.open(self.site_url, 1)
        print(self.count)
        self.count += 1
        time.sleep(self.interval_time)
        Clock.schedule_once(self.update)
        if MainScreen.run_flg:
            th = threading.Thread(target=self.SiteAccess())
            th.start()
        else:
            print("end")

    def buttonClicked(self):
        self.text = 'OK'
        self.count += 1
        self.site_url =  self.ids["text_url"].text
        self.interval_time =  self.ids["text_time"].text
        th = threading.Thread(target=self.SiteAccess())
        th.start()
    
    def buttonClicked2(self):
        global run_flg
        MainScreen.run_flg = False

    def update(self):
        self.ids.text_count.text = self.count
    
    
class TicketApp(App):
    def __init__(self, **kwargs):
        super(TicketApp, self).__init__(**kwargs)

    def build(self):
        return MainScreen()

if __name__ == '__main__':
    TicketApp().run()

<MainScreen>:
    BoxLayout:
        orientation: 'vertical'
        size: root.size
        BoxLayout:
            size: root.size
            pos: root.pos
            size_hint_y: 10
            Label:
                id: label1
                size_hint_x: 20
                font_size: 16
                text: "SITE URL :"
                canvas.before:
                    Color:
                        rgba: .68, .73, 1, .5
                    Rectangle:
                        pos: self.pos
                        size: self.size
            TextInput:
                id: text_url
                size_hint_x: 80
                font_size: 16
                text: "http://reserve.tokyodisneyresort.jp/"
                foreground_color:1,0.5,0,1
                #canvas.before:
                #    Color:
                #        rgba: .68, .73, 1, .5
                #    Rectangle:
                #        pos: self.pos
                #        size: self.size
        BoxLayout:
            size: root.size
            pos: root.pos
            size_hint_y: 10
            Label:
                id: label2
                size_hint_x: 20
                font_size: 16
                text: "interval time :"
                canvas.before:
                    Color:
                        rgba: .68, .73, 1, .5
                    Rectangle:
                        pos: self.pos
                        size: self.size
            TextInput:
                id: text_time
                size_hint_x: 20
                font_size: 16
                foreground_color:1,0.5,0,1
                text:"5"
                #canvas.before:
                #    Color:
                #        rgba: .68, .73, 1, .5
                #    Rectangle:
                #        pos: self.pos
                #        size: self.size
            Label:
                size_hint_x: 60
                font_size: 16
                text: "(sec)"
                text_size: self.size
                halign: 'left'
                valign: 'bottom'
                padding: 10,10
                canvas.before:
                    Color:
                        rgba: .68, .73, 1, .5
                    Rectangle:
                        pos: self.pos
                        size: self.size
        BoxLayout:
            size: root.size
            pos: root.pos
            size_hint_y: 10
            Label:
                id: label3
                size_hint_x: 20
                font_size: 16
                text: "access count :"
                canvas.before:
                    Color:
                        rgba: .68, .73, 1, .5
                    Rectangle:
                        pos: self.pos
                        size: self.size
            Label:
                id: text_count
                size_hint_x: 80
                font_size: 16
                text: str(root.count)
                canvas.before:
                    Color:
                        rgba: .68, .73, 1, .5
                    Rectangle:
                        pos: self.pos
                        size: self.size
        BoxLayout:
            size: root.size
            pos: root.pos
            size_hint_y: 70
            Button:
                id: button1
                text: "Run"
                font_size: 68
                on_press: root.buttonClicked()
            Button:
                id: button2
                text: "Stop"
                font_size: 68
                on_press: root.buttonClicked2()