Let's say a major portion of the shel yad parchment is so badly damaged that it cannot be fixed. But there is a section containing a full parsha that could be used as one of the parts for the shel rosh. Can one cut out that section of parchment from the shel yad and put it into the shel rosh?
Yes, you can. (ShA OC 42:1, MB ibid. sk 5)
However you could not take parts of the Tefilah Shel Rosh to use for the Tefilah Shel Yad as that would be lowering its level of holiness (ibid.), unless you specifically stipulated such when you first made the Tefilah Shel Rosh (ibid. 42:2).
Note that in an individual Tefilah, each letter of all four parshiyot must be written in order (first line in Mishnat Sofrim). So if you do start moving around parshiyot you have to make sure you know when each was written to ensure that the correct order is maintained.