The problem is not that the water is moving into another basin, it's exactly as you described. Gone. The water you put in evaporates, and is gone. That becomes water that can't recharge the tributaries. Water that can't refill the great lakes.
But all this is talk. You seem to be a person who prefers concrete evidence. So, allow me to redirect your attention to another nation who decided diverting water was no big deal, and the fruits of their labor. The country is the Soviet Union, and result is the Aral Sea. They too diverted water, albeit rivers, to the desert to grow crops. What was the result? Salinity in the Aral sea jumped tenfold while the water collapsed to a fifth of what it was before they began. Now, the sea itself has become a desert, with regular dust storms whipping through. The rivers themselves dried up, with no water to recharge them, crops began to fail with a lack of water and rising CO2 levels. This is why Michigan, seven other states, and Canada have all decided the water should not leave their basins. Of course, your farm is so important. So never mind, let the construction begin.