Ibidem is only used immediately beneath or next to what it is repeating, so there can never be any doubt as to which work it refers to. With that respect I see no problematic ibidem in your examples. If there could possibly be any doubt, do not use ibidem.
If there are two works whose titles are too similar, you must always add the author when referring to either work.
If a book should be titled Ibid. or Ibidem, which may perhaps exist, you would simply add the name of the author. If there is no author, either use [anonymous] or a description of the context in which the work was conceived, like The Priapic Society of Berlin. If two anonymous works titled Ibidem should exist, add the date, place, or editor to distinguish between them. If two works with the same title should appear on the same day with the same editor, use a distinctive phrase from the first page as a subtitle, as in Papal bulls (like In Nomine Domini from 1059) or psalms. If the contents of the two works should be wholly identical, it doesn't matter which one you refer to.
I hope you will be able to sleep tonight with this advice.
[Edit:] Note that ibidem ought to be used only to refer to a work physically next to (and preceding) it. Referring to a work mentioned on the previous page or to a couple of notes back on the same page is unacceptable. One can only add in Ibidems after the lay-out of your book/article has been finalised (if added by hand). I was also taught that "Jones, ibid., 234" is bad practice. Lastly, I often see "Jones (1921), 234", which I think is annoying, because a year is too meaningless and does not serve to identify the work: one should use short titles there ("Jones, Ostracised, 243").
There is a device that often appears in Hebrew writings known as chiastic structure. Essentially it extends chiasmus (a common literary device that relates clauses in criss-cross fashion—think "the first shall be last and the last shall be first") to an entire passage. It is particularly common in Old Testament writing. Another word used to mean chiastic structure is palistrophe.
For example, a palistrophe or chiastic structure may have the form ABCDEDCBA, meaning that an idea A is presented, followed by an idea B, and so on. Thus the first idea presented is also the last. Other chiastic structures are possible, but they are still structured so that the first and last ideas are the same (or, at the very least, similar).
I think chiastic structure appropriately describes what you are seeking.
Added: a link to a picture of the chiastic structure of Genesis 6–9 for reference.
Best Answer
Yes; this technique is known as a title drop¹.
From TVTropes, for example:
That article also explicitly lists your quote as an example of a title drop under the heading of "live action TV":
TVTropes also offers name drop as an alternative title, but because that is a well-established term outside of film and theater circles, with a different meaning, it's probably best to stick with the descriptive, direct, title drop.
¹ Which is either straightforward or unimaginative, depending on your perspective. But in either case it gets the idea across.