I hope you don't mind me adding my thoughts to the washing of feet.
Here we are talking of beautiful feet, and must think of the feet as pertaining to walking. Romans 10:15. How beautiful are the feet of them that preach the gospel of peace, and bring glad tidings of good things!
Hopefully I can point your thinking to our feet being cleaned associated with our walk in Christ.
John 13:5 After that He (Jesus) poureth water into a bason, and began to wash the disciples' feet, and to wipe them with the towel wherewith he was girded.
John 13:8 Peter saith unto him, Thou shalt never wash my feet. Jesus answered him, If I wash thee not, thou hast no part with me.
John 13:9 Simon Peter saith unto him, Lord, not my feet only, but also my hands and my head.
John 13:10 Jesus saith to him, He that is washed needeth not save to wash his feet, but is clean every whit: and ye are clean, but not all (Talking of Judas). They were all saved except Judas, but their walk needed cleaned.
What is being talked about here? We read in Ephesians 5:26 That He (Jesus) might sanctify and cleanse it with the washing of water by the word.
Ephesians 6:15 And your feet shod with the preparation of the gospel of peace; (Again the word) Even our armor is dependent upon the word. Our walk or feet shod with the word makes our walk beautiful.