singular or plural verb with 'more than one'

[Lycen]

Should we use a singular or plural verb with 'more than one'?

E.g.
There is/are more than one way...
More than one person has/have...

[Mister Micawber]

There is more than one way...
More than one person has...
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Native English teacher at Mister Micawber's

[Lycen]

That's counter-intuitive as 'more than one' is plural. Is any grammar website to properly explain this? Thanks.

[Mister Micawber]

According to the American Heritage Dictionary of English Usage:

When a noun phrase contains more than one and a singular noun, the verb is normally singular: There is more than one way to skin a cat. 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.

[Note also: Fewer than two cookies remain in the jar. Counterintuitive?]
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Native English teacher at Mister Micawber's

[Lycen]

What about this?

One of your friends is welcome. (Grammatical rule: "singular verbs to non-plural nouns and plural verbs to plural nouns")

But,

Either of your friends are welcome. (Proximity rule? i.e."choose a verbal form to agree to the form of the nearest noun in the subject noun phrase")

[Mister Micawber]

We're not talking about those formations here, though. Or are you changing the subject?
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Native English teacher at Mister Micawber's

[Lycen]

It seems that 'more than one... is' follows the proximity rule like the 'either of your friends are' example; 'either' means singular.