Why does the order of applying advice matter?

org-icomplete is a function that calls ido-completing-read (icr). Instead, I want it to call my function: ido-completing-path-like-read (icplr). This would be easily implemented as advice, except that icplr calls icr, so another advice needs to be applied to icplr to resore the original definition of icr before it is called, to prevent an infinite recursion.

I implemented this in two ways, one of which works, and one of which doesn't - icplr goes into an infinite recursion, calling itself instead of icr. Why does the one not working, not work?

Works:

(defadvice org-icompleting-read (around ido-path-like-completion activate)
  (let ((sh/orig-ido-completing-read (symbol-function 'ido-completing-read)))
    (unwind-protect
        (progn
          (defadvice ido-completing-path-like-read
            (around save-ido-completing-read activate)
            (setf (symbol-function 'ido-completing-read)
                  sh/orig-ido-completing-read)
            ad-do-it
            )
          (setf (symbol-function 'ido-completing-read)
                (symbol-function 'ido-completing-path-like-read))
          ad-do-it
          )
      (setf (symbol-function 'ido-completing-read)
            sh/orig-ido-completing-read)
      (ad-remove-advice 'ido-completing-path-like-read 'around 'save-ido-completing-read)
      ))
  )

Does not work:

(defadvice org-icompleting-read (around ido-path-like-completion activate)
  (let ((sh/orig-ido-completing-read (symbol-function 'ido-completing-read)))
    (unwind-protect
        (progn
          (setf (symbol-function 'ido-completing-read)
                (symbol-function 'ido-completing-path-like-read))
          (defadvice ido-completing-path-like-read
            (around save-ido-completing-read activate)
            (setf (symbol-function 'ido-completing-read)
                  sh/orig-ido-completing-read)
            ad-do-it
            )
          ad-do-it
          )
      (setf (symbol-function 'ido-completing-read)
            sh/orig-ido-completing-read)
      (ad-remove-advice 'ido-completing-path-like-read 'around 'save-ido-completing-read)
      ))
  )

Edit

1. I want to make it clear that all the mentioned functiond: ido-completing-path-like-read, ido-completing-read, and org-icompleting-read are to be treated (and two of them in fact are) library functions, the definitions of which I do not control.

2. While I'm open to suggestions for alternative patterns here and would appreciate those, I will only accept an answer that actually answers my question: Why does the first code work and the second doesn't? Thanks for understanding.