Removing a House’s Mezuzos

A renter is obligated to affix a mezuzah just as a homeowner is. However, most Rishonim are of the opinion that a renter’s obligation is only rabbinic. The Gemara (Bava Metzia 102a) notes that a renter may not remove his mezuzos when he vacates his rental. The Gemara proceeds to cite a story about a renter who removed his mezuzos when he moved elsewhere. The consequences were disastrous.
The Gemara cites a major exception to the aforementioned halacha. If the next tenant or owner will be someone who will disgrace the mezuzos, then they should be removed.
The Rishonim note that the Amora Shmuel rules that one may remove tzitzis strings from one garment and affix them to a different garment. The halacha should be the same as a mezuzah. Why may the renter not remove his mezuzos and affix them elsewhere?
There are (at least) four answers to this question. Rav Achai Gaon posits that the premise of the question is one hundred percent correct. The halachos of mezuzos and tzitzis strings are the same. Both may be removed and affixed elsewhere. However, one may not remove a mezuzah and put it in a display case. One may not remove kosher tzitzis strings from a garment and put them in a drawer. This is considered disgracing the mitzvah. Therefore, the renter may indeed remove his mezuzos from his old apartment as long as he puts them up in his new one.