From the literal perspective, the truth whispered in the ear, are we literally to proclaim that truth from the roofs? What I tell you in the dark, speak in the daylight; what is whispered in your ear, proclaim from the roofs. (Matt 10:27 NIV)

--> THIS IS THE QUESTION: From the literal perspective, the truth whispered in the ear, are we literally to proclaim that truth from the roofs considering other biblical perspectives including but not limited to the following verses?

For this literal perspective I find:
"So do not be afraid of them, for there is nothing concealed that will not be disclosed, or hidden that will not be made known." (Matt 10:26 NIV), "... now something greater than Solomon is here." (Matthew 12:42 NIV), "For lack of wood the fire goes out, and where there is no whisperer, quarreling ceases." (Proverbs 26:20 NIV).

Against this literal perspective I find:
"A gossip betrays a confidence, but a trustworthy person keeps a secret." (Proverbs 11:13 NIV), and "A gossip betrays a confidence; so avoid anyone who talks too much." (Proverbs 20:19 NIV), and "Besides that, they learn to be idlers, going about from house to house, and not only idlers, but also gossips and busybodies, saying what they should not." (1 Timothy 5:13 NIV).

Or is it not Gossip, because it fully known what is being said?
How Literal?

Is the "literal perspective" well defined? On the one hand, if everything is taken strictly literally, things just don't make sense. There are contradictions. At the other extreme, if nothing is meant to be taken literally, everything is ambiguous. If you assume that the message of the Bible is actually true and meant to be taken seriously, there has to be a position in the middle, and I don't know if that qualifies as the "literal perspective."

Perhaps a useful question to ask about how to read a passage is, "Does this make sense if it is understood literally?" or "To what extent is this meant to be taken literally?" If you look at the broader context of the passage, or the Bible as a whole, is there any conflict with a strictly literal interpretation? A literal interpretation is the default, but it is not always the correct way to understand what's written.

Your question about Jesus' command in Mt 10:27 is about how to reconcile this statement with other passages if it is to be taken literally. I will try to answer a similar question: How literally should we take Jesus' command in Mt 10:27?

But first,

Proverbs

Proverbs cannot reasonably be assumed to be a compendium of ubiquitously applicable, absolute assertions. It is a collection of wise sayings that, at least, are generally true, if not always true. Any given maxim may be always true, but it doesn't have to be just because it's included in the book. For example:


  Proverbs 26:5-6 (NASB)
  Do not answer a fool according to his folly, Or you will also be like him.
  Answer a fool as his folly deserves, That he not be wise in his own eyes.


These two things cannot both apply in all situations. A strictly literal interpretation of these two maxims (and the underlying assumption that Proverbs is full of statements that are always absolutely applicable) is nonsense.

Your use of Proverbs in harmony and disharmony with Jesus' command is not a Safe Way™ to use Proverbs. Without justifying that a given proverb is genuinely applicable and unilaterally binding on the situation that Jesus is addressing, it is exegetically risky to put those two statements together (or compare them for disharmony—something Biblical critics waste a lot of time doing).

Is it Reasonable?

In Matthew 10, Jesus is sending the disciples out on a specific task, and is giving them advice (and commands). If we read the pieces of his commands strictly literally, he might be telling us never to keep secrets. But, does that make sense? No. The wisdom in the other verses you pointed out says as much. To read his words this way creates a contradiction. If we're proceeding from the assumption that the Bible is true and makes sense, we cannot accept this reading.

An Alternate Reading

This might be debatable, but when I read his words,
"What I tell you…" and then "what you hear whispered in your ear…," it sounds like they're both speaking of what Jesus will tell us (as if he is the one who will be whispering in the disciples' ears). The context of this passage has nothing to do with gossip or bad habits. It has nothing to do with secrets. It's about these disciples going out to proclaim the message to everyone. Earlier in Jesus' address, he says, "do not worry about how or what you are to say; for it will be given you in that hour what you are to say." The context of the "whisper" points to Jesus/God/the Holy Spirit telling the disciples what they should say. They will hear it "whispered in [their] ear," and they are to "proclaim [it] upon the housetops."