Ah, proverbs! Morality for the lazy. How else can you sum up the wisdom of the ages in one pithy phrase? Unfortunately, they’re not always consistant. For example, there’s “Haste makes waste”, but, “He who hesitates is lost”. “Business before pleasure”, but “all work and no play makes Jack a dull boy”.
So, how many other dueling proverbs can you find?
Out of sight, out of mind vs Absence makes the heart grow fonder. 
(Similar to the first pair you quoted)
“Look before you leap” “The race is to the swift”
“Two heads are better than one” vs. “Too many cooks spoil the broth.”
“Live by the sword, die by the sword” vs. “Be careful, you’ll put your eye out with that thing!”
“The squeaky wheel gets the grease.”
vs
“The nail that sticks up gets pounded down.”
Tomorrow is another day vs. Live each day as if it were your last.
You do realize that not all of those proverbs quoted are diametrically opposed?
Also, they don’t intend to explain the universe or even make a coherent worldview for anyone to follow, so expecting them to is kind of pointless.
But whatever.
I know…it’s just a game, that’s all.
How about “Consistency is the hobgoblin of small minds?”
The devil is in the details!
With these two quotes in mind, I’d just like to point out that the proverb is: “A foolish consistency is the hobgoblin of small minds”.
And I’d like to point you to this page which contains the text of Ralph Waldo Emerson’s essay Self-Reliance:
“They also serve who only stand and wait”, but “if you’re not part of the solution, you’re part of the problem.”
Although “the pen is mightier than the sword”,“actions speak louder than words.”
“Children should be seen and not heard”, yet “out of the mouths of babes ofttimes come gems.”