Since the Assyrians had overextended themselves by invading Egypt, their major military assets were deployed there. This weakened their borders with the Medes and Persians protected in some measure by the Northern Kingdom Israelites who were supposed to be acting as buffers. The Israelites generally got along OK with the Medes and Persians. Everyone understood the game.
But when the Assyrians got in trouble in Egypt they all saw their chance. The Israelites turned from being in the way of the Medes and Persians to joining them, and that was the beginning of the end for Assyria. The trick now was for the Israelites to get out of the way and let the others have their long desired victory over Assyria.
As you pointed out, at this point the Israelites could not escape back towards home in Canaan. So "they took council among themselves" and decided not to even try since they didn't much care for their Southern Kingdom cousins anyway. When they were anywhere close it was just fight, fight, fight. Besides, the Southern Kingdom had done them no favours with the Assyrians while they were in captivity. But that's another story for another time.
So the Israelites determined to get the Hell out of Dodge any way possible. The South & SW were blocked by the Assyrians and that war. The SE and E were blocked by the Medes and Persians who weren't real excited about having 6 MILLION Israelites traipsing through their territory on the way to who knows where. Besides, would you really trust 6 MILLION agitated Israelites to not try something funny after all those years in border tension? Only the NE, N and W were open for escape.
So "with great noise and confusion" it took "a year and a half" for MILLIONS of Israelites with their possessions to "pass through the headwaters" of the Tigris and Euphrates and make their way north through the Darial Pass (aka the Caucasian Gates) in the Caucasus Mountains. From there they headed west and northwest toward the otherwise mostly uninhabited area we call the Ukraine and Russian Steppes.
Most of the others went west past Lake Van and along the south coast of the Black Sea. Hundreds of years later some of their offspring as The Lost Sheep of the House of Israel were met by and corresponded with the Apostle Paul at places like Corinth, Phillipi, Galatia and Ephesus.
A few other Israelites escaped to the NE around the Caspian Sea. It is speculated that some of these may be ancestors of the Caucasians which are found in China. All in all, this was probably the greatest migration in the history of man.
>there had to be a lot of Israelite fighting men,
The largest military armada in world history was comprised of American, Canadian and British forces which landed at Normandy with 156,000 men on the first day. 25 days later total Allied forces landed in France was 660,000. The Israelites had 1,000,000 (1 MILLION) fighting men. We have to assume the Assyrians, Medes and Persians had even more. With all that vacant (and free) land available in uncharted, undeveloped and unpeopled Europe no wonder they heard the call of the west.
We know of no Century 21 or ReMAX offices in the Caucasus at that time, but there were undoubtedly Assyrian and other traders who traveled the routes and brought back stories. After all, the proto-Celts, the Israelites much older Israelite cousins from Egypt and Caanan were already busy at Hallstadt, Austria and elsewhere. The Assyrians were great business men and their was society quite developed for the time. They had one of historys great libraries at Ninevah where the 23,000 Assyrian Tablets were kept. Assyrians regarded business activity as so important to the economy that businessmen were exempt from Assyrian military service.
>which you x6 to get the total population including women, children, old folks, infirm, crippled, and nother non-combatants.
Some historians, archeologists and anthropologists include slaves in the x6, while others fudge it with a more arbitrary x7 to allow for possible slaves. Yes, the Bible says some Israelites did have slaves, we just don't know how many. In the course of history it was not uncommon for even some slaves to have slaves. How terribly un-PC that is to learn, but then we are shattering one delusion after another! {ggg}.
Owning slaves was far from the worst of the transgressions of ALL of the Israelites. That is, after all, why the North was being punished! It wouldn't be long until the South got theirs.
It is frustrating to contemplate the huge size of the "combined" 10 tribes which made up the Northern Kingdom in light of their erratic success in military ventures. The Romans and others noted (later) that while putting on a good act with naked warriors painted in bright colors, etc., these Celts were the gang that couldn't shoot straight. As great artists and craftsmen they seemed to be better lovers than fighters. They would rather argue than fight.
The Assyrians by contrast were great organizers and businessmen, and fierce warriors, a deadly combination weakened only by overconfidence. By sheer military skill (blitzkreig?) the Assyrians nibbled away at the Northern Kingdom in Canaan removing it piece by piece (perhaps tribe by tribe) over the years while the disorganized Israelites debated. A very much smaller but skilled Assyrian force could have prevailed both in the initial conquest and in keeping the Israelites under control as a buffer between the Medes and Persians. It doesn't take much of a force to keep unarmed and debilitated prisoners under control.