grammar - Meaning of と in 友蔵が出おくれまいと言いそえた

「わしもじゃ」
友蔵が出おくれまいと言いそえた。
"Me too" added Tomozou, not wanting to get a late start.

So I eventually figured out that まい was negative volitional (I hope I'm right) then got stuck thinking that と was quotative and couldn't make any sense of it. The context doesn't really fit with him saying that he won't get at late start

I'm now thinking that と is actually making the previous phrase adverbial, resulting in my above translation. Have I got this correct?

Answer

You can think of the ～まいと as ～まいとして.

～うと・～ようと ⇒　～うとして・～ようとして "trying to~~"
～まいと ⇒　～まいとして "trying not to~~"

Examples:

• 子供を助けようと川に飛び込んだ。⇒ 子供を助けようとして川に飛び込んだ。


• 涙を見せまいと背を向ける ⇒ 涙を見せまいとして背を向ける