Greater Lake Nipigon is good (fits into existing geomorphology) but I'm wondering if 'Lake WisIll' is a starter.
Putting it there, you're going to have to
1) move the Mississippi basin over a bit, or
2) either have the Big Muddy drain into the Great Lakes or
3) some of the Great Lakes drain to the Gulf of Mexico
With 2, you still have the Missouri watershed going to the Gulf of Mexico, so it's still one of the longest Rivers in the world.
With 3, it's probably not all of the great lakes. Depending on the elevation of the new lake and it's connection to Michigan, you could get just Michigan, or Michigan + Huron + Superior draining into it, with Lake St. Claire have outlets going both ways. Erie and Ontario will still go down to the Atlantic.
Of course, anywhere you put the lake will mean shifting some basins around.
I think your best bet is to have a POD early in the ice age with a modified glaciation, although this is difficult to do as well. What would happen if the driftless area weren't driftless? Could you even get the driftless area to not be driftless?
Looking at improving rainfall in the Midwest we are, see?
I'm not all that certain that the Great Lakes really effect rainfall that much. I'm no climatologist, though, but it seems to me that most of the humidity we get comes up from the Gulf.
Besides, unless by Midwest you mean the Great Plains, there generally isn't much need for more rainfall here.
This is very true, but I'm not sure what the exact effects would be. Does anyone know how various native groups used the lakes? I would assume that an additional lake would increase communication and trade.
All I can tell you is that the lakes were a significant 'highway' of trade and migration for Native Americans. Depending on where you put the lake, you'll definitely see much different migrations.
The Ojibwe and the Iroquois, and several other nations which I also know little about, are very closely associated with the Lakes.
But also, look at whatever nations were into the areas where the extra lake is going to be. A WisIll lake, for example, might very well lead to a larger Mississippian Civilization expansion into the lakes. Or, it might lead to a Siouan nation with larger influence in the Great Lakes.
This, of course, assumes you can trap enough butterflies to make these nations still exist.