While reading researches that others have made like this good answer on ELL or this Grammarexchange post, it becomes apparent that singular is always preferred after more than one, though much less after more than one of.
Looking in the CAGEL, I have only found a comment on the grammatical behaviour of more than one followed by singular nouns. Neither is there any reference to more than one of the +plural noun in the Comprehensive Grammar of the English Language. Quirk only notes:
Grammatical concord is usually obeyed for more than, though it may conflict with notional concord:
- More than one member has protested against the proposal.
Although the subject is notionally plural, the singular is preferred because member is analysed as head of the noun phrase. (p. 758)
In order to understand how the choice of singular or plural can even possibly fluctuate, this post of a native speaker sheds some light:
In English the subject-verb concord is basically made up of mixture of three rules: (1) grammatical rule, (2) notional rule and (3) proximity rule.
- (1) The grammatical rule is "singular verbs to non-plural nouns and plural verbs to plural nouns".
[EX] This apple is delicious but those lemons are sour.
[EX] English is a tough language to learn.
- (2) The notional rule is "use plural verbs when we can feel in a non-plural noun more than one person".
[EX] The audience have got tired of his speech.
- (3) The proximity rule is "choose a verbal form to agree to the form of the nearest noun in the subject noun phrase".
[EX] Either of your friends are welcome.
These three rules often conflict each other and the priority for the choice in such a case can vary depending on speaker.
I guess, as to "more than one of my students are American", you are choosing the verbal form according to the proximity rule, and you say "more than one student is American" according to the grammatical rule rather than to the notional rule.
The rule about more than one + of the + plural noun requiring a verb in the plural is encountered on grammar sites on the internet. For example the English Language Help Desk seems to agree with Grammarphobia you have quoted:
(9) More than one scientist is trying to find a cure for HIV.
Example (9) is indeed surprising – there are obviously many scientists who try to find a cure for HIV, but the verb is still singular. The reason for this is that one is always followed by a singular noun (one scientist), and the verb agrees with this singular noun.
A tiny change to the expression more than one changes the agreement on the verb.
(10) More than one of the scientists working on a HIV-cure believe in a prompt breakthrough.
The Word spell-checker claims that one needs a singular verb in (10). The spell-checker is wrong. When more than one is followed by of and a plural noun, the verb is plural.
As a reputable source who clearly deals with this matter, I have only found The American Heritage Dictionary which provides this Usage Note:
When a noun phrase contains more than one and a singular noun, the verb is normally singular:
- More than one editor is working on that project.
- More than one field has been planted with oats.
When more than one is followed by of and a plural noun, the verb is plural:
- More than one of the paintings were stolen.
- More than one of the cottages are for sale.
When more than one stands alone, it usually takes a singular verb, but it may take a plural verb if the notion of multiplicity predominates:
The operating rooms are all in good order. More than one is (or are) equipped with the latest imaging technology.
Do note the use of usually in this explanation, which shows that the AHD does not state it as an absolute rule.
My conclusion is that, when more than one is followed by of the + a plural noun, as some comments have shown, I guess it is better to go with your intuition. One of the three rules (grammatical, notional or of proximity) will back you up.