Would there be a comma after the year here? As this is a series of prepositional phrases, I am uncertain that the comma should be inserted.
The composer was alleged to have said this to his secretary in 1940, about a seasonal song.
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"He said 'Not now.'" I couldn't find an answer I'd feel comfortable definitively quoting, but here and here are what I could find.
"I feel tempted to say 'Just drive' like they do in movies." No, you don't need to put a comma there. My feeling is that in theory you could put one, depending on the context, but you're better off without. I don't think it should be capitalized either.
"E.g. 'I'll be there in ten minutes,' he said." Indeed, if you don't have any other closing punctuation you should put a comma in.
There a couple of misconceptions here. The first is about reduced participial phrases. Generally this means transforming a clause, which has a finite verb, into a phrase with a non-finite verb. Thus
I came to work today while I was wearing my new suit
becomes
I came to work today, wearing my new suit
Secondly, I don't know what grammar is telling you that participial phrases have to modify adjectives. Participial phrases may act as modifiers for any construct that can take a modifier.
Next, I'm not sure what you think a "participial prepositional phrase" is. One example you give is
- This is good result(,) given how other teams performed
but there isn't a preposition in sight.
Participles by themselves don't really carry tense. You seem to think there's a difference in punctuation based on whether there's a present participle (one that ends in -ing, e.g., "coming home") or a present perfect participle (one that combines having with the plain form of the verb, e.g, "having come home"). There isn't.
Most of your examples may be parsed as nominative absolutes. For example,
I came to work today, wearing my new suit.
These aren't really restrictive or non-restrictive because they are independent of the grammar of the main clause (thus the name absolute). The wearing of the new suit applies not just to the subject, verb, or prepositional complement individually. The style manual I use, the Chicago Manual of Style recommends setting off introductory elements like this with a comma. CMOS also recommends setting off following non-restrictive elements with a comma, so I infer the same for following absolutes.
Punctuation is a matter of style, not grammar. So follow the rules in the manual of style that you've chosen or that has been thrust upon you.
Best Answer
Is a comma needed after the year 1940?
The sentence follows: The composer was alleged to have said this to his secretary in 1940, about a seasonal song.
Following the principle that one should avoid breaking up the flow of a sentence as much as possible--and this includes unnecessary commas--it would make sense not to place a comma after 1940. Certainly it is not necessary.
Perhaps even better would be a simple relocation of the prepositional phrase to the beginning of the sentence, such as this: In 1940 the composer was alleged to have said this to his secretary about a seasonal song.