What was Garner thinking?
With regard to the sentence
The Bruce Willis supernatural thriller has grossed $20 million for the fifth consecutive weekend, accomplishing what no other film has done except ‘Titanic’.
Garner takes the position that either "no film other than" or "no film except" suffices to identify the unnamed film in question (Die Hard With a Large Bank Account, or whatever it may be) as a second exception to the rule applying to all films besides the reference film (in this case, Titanic).
If we accept the premise that "no X other than" and "no X except" are the two standard stools that English invites us to perch our negative exception language on, it would seem that "no other X except" falls between those two stools—neither completing the first properly nor landing on the second with proper succinctness.
Later in the same entry for "No other ... than," Garner identifies an instance in which, in his view, "no other... except" is logically correct:
Very occasionally, the no other ... except phrasing is actually correct—e.g.: "Vojtas has testified repeatedly that he earned less than $50,000 a year as a police officer and that he had no other source of income except for gifts from his mother." [Citation omitted.] Here the word other refers to something already mentioned (the $50,000 salary), as opposed to referring to something in a yet-to-be-completed than clause.
So it seems clear that Garner objects to "no other X except" on grounds that, on the one hand, it overdefines an instance in which "no X other than" or "no X except" would suffice to indicate that one thing alone is an exception to the blanket "no," and, on the other hand, it misuses a formulation that has a definite and correct meaning in certain rare cases (such as the "Vojtas" quotation that he discusses near the end of his coverage of the wording).
However, Garner's treatment doesn't squarely address the question of whether "no other X except" deserves to be treated as a third legitimate stool, coequal with "no X other than" and "no X except," on the strength of its frequent (and longtime) idiomatic use in English.
Early grammatical discussions of 'no other X except'
Observers have long been aware of the logical complexity of accurately expressing negative ideas in phrases that include the word other, such as no other than, "no other but," "no other besides," and no other except One interesting early discussion occurs a brief chapter titled "No Other Besides. No Other Except. No Other But." in Robert Baker, Remarks on the English Language], second edition (1779 [the first edition came out in 1770):
If I ask a friend what visits he has received to-day, and he would signify that Mr. A is the only person that has visited him, he may say No person besides Mr. A has visited me, or no other person than Mr. A has visited me. But to say no other person besides Mr. A has visited me, would be wrong, because it would seem as if somebody else had been mentioned before the mention of Mr. A.
Where the words no other have a reference, this expression may be right.
If I say Mr. A and Mr. B have called on me to-day : but no other person has come into my room, besides my taylor, (or excepting my taylor) herein there is nothing improper. The words no other have here a meaning ; whereas in the former instance they have none. They signify no other person than Mr. A and Mr. B.
In poetry, the sort of expression here condemned seems sometimes to give force which would otherwise be wanting. When that is the case, it may be allowed.
This last concession is really quite extraordinary: "no other X except is illogical when applied to a single exception, but when used poetically it can supply needed force and therefore may be allowed.
In any case, half a century later, Alexander Crombie, Etymology and Syntax of the English Language (1830) raises the same issue and seems not entirely persuaded by Baker's reasoning:
"The Romans had no other subsistence but the scanty pillage of a few farms." Other is redundant; it should be, "no subsistence but," or "no other subsistence than." In the Saxon language, and the earlier English writers, the word other is not universally followed by than, but sometimes with but, before, save, except, thus, Mark, xii. 32, "thær an God is, and nis other butan him," thus rendered in the Bishops' Translation, "there is one God, and there is none but he." In the Book of Common Prayer we have, "thou shalt have no other gods, but me ;" and the same form of expression occurs in Addison, Swift, and other contemporary writers. Usage, however, seems of late to have decided almost universally in favour of than. This decision is not only consistent with analogy, if the word other is to be deemed a comparative, but may also, in some cases, be subservient to perspicuity. No other but, no other beside, no other except are equivalent expressions, and do not perhaps convey precisely the same idea with none but, no other than. Thus if we take an example similar to Baker's, and suppose a person to say, "A called on me this morning," B asks, "No one else?" "No other," answers A, but my stationer." Here the expression, as Baker remarks, seems strictly proper, the words no other having a reference to A. But if the stationer had been the only visitor, he [the person speaking to B] should say, "none but," or "no other than the stationer called on me this morning." This is the opinion of Baker. The distinction, which he wishes to establish, is sufficiently evident; but that it is warranted by strict analysis, I do not mean to affirm.
That Garner—whom I take to be a practical and fair-minded modern usage authority—adopts the 1779 Baker line with regard to the illogic of "no other X except" surprises and intrigues me. He seems to be reacting to two things: the fact that the simpler, uncontroversial wordings "no other X than" and "no X except" remain at least as common as "no other X except," and the possibility that illogical use of "no other X except" may undercut logical (and therefore proper) use of the phrase.
But Garner would, I think, readily concede that illogic by itself is no absolute bar to common (and indeed standard) usage in English. English speakers have been using the expressions "no other X except," "no other X but," "no other X besides," etc., in the now-disapproved sense for a very long time—certainly long before the language more-or-less standardized on "no other X than," according to Alexander Crombie, writing in 1830.
Under the circumstances, it's hard to view Garner's argument from logic against "no other X except" as being much more than the perpetuation of an ancient academic solution to an old riddle. As Crombie wrote 187 years ago, "The distinction, which he wishes to establish, is sufficiently evident; but that it is warranted by strict analysis, I do not mean to affirm."