Can you omit the action when using と and help understanding/parsing this sentence

Question

『監視されているみたいだ』と不評の声も多い見回りだけど, 案外さっきみたいな事柄のためにやっているのかもしれないな。

The complete sentence is given above. As the title has said, can you omit the action when using と? From some sentences I've seen, an action verb often accompanies と when used with direct quotes. I am aware of って being used as a casual quoting particle where we can omit other parts of the sentence but can that also be applied for と when used with direct quotes?

If that is so then, would it go『監視されているみたいだ』という不評の声... and mean something like

"The numerous watchmen are also like the (unpopular) voices saying 'It seems like we're being watched' but/and..."

Like a simile/metaphor? My attempt at translation would then be (not that it makes much sense)

"The numerous watchmen are also like the (unpopular) voices saying 'It seems like we're being watched' and It might be because of unexpected things like earlier happening."

Maybe I'm misinterpreting the と？ I haven't had much experience with sentences like this and even with context I could barely understand the statement. This sentence is probably way above what my current abilities are capable of understanding and that any help pointing me in the right direction would be appreciated.

For some context, the previous scene was showing the student council doing their routine patrol when they stumbled upon an incident involving the speaker and the current scene is a narration.

Answer 1

I think your comprehension of 「と」 is correct.

『監視されているみたいだ』と不評の声

『監視されているみたいだ』という不評の声

These 2 phrases are basically the same as you inferred.

The tree of this sentence is like below.

NPだけど, 案外さっきみたいな事柄のためにやっているのかもしれないな。

(NP = Noun Phrase)

Here, "NPだけど" means "Regarding NP", "As for NP", or something like that. To make clear we often use "NPについてだけど、", "NPに関してだけど" but sometimes they are omitted. Thus you could translate this like "Regarding NP, it might be because of unexpected things like earlier happening."

The NP in this sentence is "『監視されているみたいだ』と不評の声も多い見回り". And the head of this NP is "見回り"(watchmen) as you assembled. But you missed another point!! 多い is modifying "不評の声" here, not watchmen!! "-の声も多い" is kind of phrase meaning "It is frequently said as -".

Thus the whole translation is like this.

Regarding watchmen who are often blamed as "It seems like we're being watched", it might be for the things like the earlier happening, against my expect.