grammar - When is 「だ／である」required between a noun and the quotation particle と?

Note: Edits in response to comments have been added in italics

The sentence prompting this question is:

時下ますますご清栄のことと、お喜び申し上げます

Which I have always "loosely" taken to mean:

I am glad to hear you are doing so well these days.

Based on the explanation of と　on page 464 of "A dictionary of intermediate Japanese Grammar", I think there is an ellipsis of 伺いまして, and hence is quotive but I am not entirely sure.

But to return to my question, when is 「だ／である」required between a noun and the quotation particle と?:

There some straight forward cases that are easy to remember such as (1)with names (2) direct quotes and (3)"fixed expressions"　such as "とばかり”:

(1) Tim と言います| I am called Tim　

(2)「＿＿＿＿」と言います。｜normal direct quote　

(3)負けじとばかりゴールを目ざして走った｜Determined not to be beaten, he dashed toward the goal.

I also found the advice in the Dictionary of Basic Jpse Grammar that in the sentence:

米国の貿易赤字は しばらくのまま 続く もの と 予想される。 It is predicted that the US trade deficit will remain as it is for a while.

"Mono followed by a quotative と is used in general statements or opinion. This mono could be dropped without a change in meaning. Note that copula だ does not follow と."

But when making my own sentences of indirect quotes (etc?) it is not so straightforward because I am not sure what rule/principle applies.

Could somebody some insight on when the copula (だ）particle と　go together?

(If sentence 3 is based on the same principle as sentence 2 then perhaps I have covered all the expceptions?)

Answer

I think it is simply an issue of whether you are quoting a complete sentence or not.

ティムと言います。
He is called Tim.

ティムだと言っています。
It's being said that he is Tim.

As quoting particle, と is allowed to quote anything. But there are other uses of と, like the conditional と, the AとB(と) construction for "and", and the と of と-adverbs (like 負けじと of the third sentence), which I would say is related to the と of the mimeses like じっと, ちらっと, which are also adverbs.

The question of whether or not a だ・である should come before と is only relevant to と as quoting particle. For example, when an idea is presented with ということ（です）, the idea is something that should be presented as a full sentence, which, when ending in a noun, should be followed by だ.

今日はお休みだということです。
It means that today is a holiday.

Quoting incomplete sentences only makes sense in appropriate contexts, for example when you give your name (where you only "quote" your name).

In English, too, quoting incomplete sentences (i.e. sentences without a verb) makes sense in few cases. The last example without a verb in the quoted sentence would render as

It means that today a holiday.

I think that both in English and Japanese indirect quotes should always be full sentences, i.e. in this case, in Japanese you should always use だ after noun phrases.

Of course, this rule may be broken for more polite Japanese, as in your example sentence:

時下ますますご清栄のことと、お喜び申し上げます。

would be a short & formal version of

時下ますますご清栄のことだと伺いまして、お喜び申し上げます。

(Of course that's not the only usual rule of grammar that polite language breaks: 申し上げる is transitive, but お喜び is not marked by を.)