I would like to know what "a sort of thought-through whisper" means in the following sentences:
‘That’s the right attitude.’ He leaned forward and put his chunky arms on the desk, his fingertips touching one another. ‘Because I cannot guarantee anything, you see. Ultimately, the board needs to accept your proposal, and they’re a tough bunch.’ He turned sideways in his chair, bent over, rummaged in a drawer. Finally, he pulled out a thin stack of papers. ‘Here, fill these out. And bring me a proposal by the end of the week. We’ll look it over together.’
Before he handed me the papers, he threw a careful look at the door, then back to me. He spoke with a lowered voice, a sort of thought-through whisper.
‘I need hardly tell you what the conditions are. Something that won’t be too upsetting, you see.’ He made a wave-like gesture with his hand. ‘Nothing controversial. Nothing remotely anti-socialist, no whiff of pro-Westernism, my dear. Recently they’ve been getting increasingly nervous about that sort of thing.’
‘I understand,’ I said, taking the papers from him.
In this novel which is set in the 1980's in Poland under the socialist regime, where homosexuality was socially unacceptable, the protagonist Ludwik (a university graduate) left Poland in 1981 to live in the United States of America. And he remembers what it was like back then in Poland, where he, now finished his studies at college and searching for his career, visited his literature professor's office and told him that he decided to apply for a doctorate after all. (He had declined his professor's proposal about the doctorate, thinking that the professor would force him to write about a topic foolish yet politically useful.) At this, his professor said "That's the right attitude," and told him things he should mind in writing his proposal for the doctorate.
In this part, I wonder what a "thought-through" whisper would mean. I looked "think through" up in the dictionary and it said "ponder upon," but I am not sure whether this meaning is applicable to the "thought-through" in this context.
I am an English learner from South Korea, so thank you for your patience in advance as I may not know obvious things. I would very much appreciate your help. :)