I am in the U.S. and I agree with User A's original versions. In Claire Kehrwald Cook's book Line By Line (which I highly recommend), Ms. Cook, writes (p. 23):
An adverb modifying a verb phrase goes after the first word in the phrase (was extremely surprised, has often been said, would certainly have asked) unless, in verb phrases of three or more words, it modifies only the participle (had been justly accused, would have been officially ruled). You usually know instinctively when to put the adverb before the participle, and when you can't be sure, the position probably makes no difference.
This passage should address your last two examples. (That is, User A's wording is preferable.)
As for the placement of also, Ms. Cook writes (p. 25):
Whatever the grammatical complexities, also—meaning "in addition"—can attach itself to a variety of sentence elements, so that you have to place it carefully to avoid false connections. What element is "in addition" in the following sentence?
I also think he is lying about where he was that night.
Do you give the same answer when you read that sentence as the second of a pair?
She doesn't believe the defendant's alibi for the night of the murder. I also think he is lying about where he was that night.
I think he hated her enough to killer her. I also think he is lying about where he was that night.
The defendant lied about his pevious marriage. I also think he is lying about where he was that night.
These examples should demonstrate that also in the normal adverbial positions can sometimes seem to modify one sentence element and sometimes another, the interpretation varying with the context. Strictly speaking, the also belongs before think only when the sentence states an additional thought, as in the second example. Substituting too for also would more clearly convey the sense intended in the first example, and in the last example also belongs between is and lying.
In your first example, Example X can also be written as Y... is fine and preferable. You're talking about two ways of writing X.
Can you point this pattern of writing and revising out to the two parties involved? It is an astute observation, and they would both benefit from knowing they have a careful collaborator in you. You might recommend Line by Line, too.