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.

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.