Genesis flood - Was it a local flood?

It seems it is not so easy to say that Noah's flood was local, yet there may be a case to be made for that.
The crucial question would seem to be: What does "the face of the whole earth" mean? Now here is an instance where this phrase is used:
Genesis 41:56 When the famine was spread over all the face of the earth, then Joseph opened all the storehouses, and sold to the Egyptians; and the famine was severe in the land of Egypt.
Yet this is not considered to be a worldwide drought, as is reflected in these other translations:
Genesis 41:56 So when the famine had spread over all the land... (ESV)
Genesis 41:56 When the famine had spread over the whole country... (NIV)
So it seems we need not conclude that this phrase always refers to the entire world.
Genesis 7:19-20  They rose greatly on the earth, and all the high mountains under the entire heavens were covered. The waters rose and covered the mountains to a depth of more than twenty feet.
Here is another difficulty, local floods don't cover mountains. Now some would say this really means "covered with rain, and not (necessarily) with water," but I don't think this will do, for mountains being covered with rain would not have been in doubt! This would not actully need stating, it would be like saying "it rained, and the mountains became wet." However, the word for "mountains" can mean either "mountains" or "hills," and this word is used for both "high hills" and "the mountains" here, it is the same word, so this could read "all the high hills were covered ... and the hills were covered."
Yet doesn't "under the entire heavens" point to a global perspective? Here is another instance of this phrase:
Deuteronomy 2:25 "This day I will begin to put the dread and fear of you upon the peoples everywhere under the heavens, who, when they hear the report of you, will tremble and be in anguish because of you."
Now need we say that every nation on earth would hear this report? That this is what is meant? It seems that a more restricted meaning may be appropriate here, with all the nations in this area, most notably the ones who would be affected, being meant.
Genesis 7:21-23  And all flesh died that moved on the earth, birds, livestock, beasts, all swarming creatures that swarm on the earth, and all mankind. Everything on the dry land in whose nostrils was the breath of life died. He blotted out every living thing that was on the face of the ground, man and animals and creeping things and birds of the heavens. They were blotted out from the earth. Only Noah was left, and those who were with him in the ark.
And now we must ask how "all flesh that moved on earth" could die in a local flood, and only Noah and those in the ark were then left. But again, these references to "the face of the whole earth" (Gen. 6:1,7;7:4,23;8:8) are consistent with a local flood, as is shown by this statement in the actual account itself:
Genesis 8:5-9  The water decreased steadily until the tenth month; in the tenth month, on the first day of the month, the tops of the mountains [or "hills," again] became visible. ... Then he sent out a dove from him, to see if the water was abated from the face of the land; but the dove found no resting place ... for the water was on the surface of all the earth.
So water being "on the surface of all the earth" does not mean there is no land above water whatsoever, for land was said to be visible at this time.
Genesis 8:4 ... and on the seventeenth day of the seventh month the ark came to rest on the mountains of Ararat.
Now in a local flood, the ark would have to float up the mountain, to reach the top of mount Ararat. The mountains of Ararat cover 100,000 square miles, though! And this does not say the ark came to rest on mount Ararat specifically, nor at or near the top of some mountain.
We may also note that a wind was sent to disperse the flood (Gen. 8:1), and then also note that this would not disperse a global flood.
However, the promise was that there would never again be such a flood, though this might mean a local flood of such proportions.