So, 美化語 is used to create honorifics: お名前 ご注文 etc.
But, the standard way to create the 謙譲語 form of verbs is: お＋[verb stem] + いたします
That does not make logical sense to modify the action that you are performing with an honorific "お", right? There is nothing about this paradox that would help with understanding 敬語 in a broader context。Every language has its idiosyncrasies. Assigning 美化語 to action you perform is just something to memorize, right? I don't care about etymology. So, memorize and move on to the next topic?