LaSalle's plan for the Griffon had been to have it unload its furs at Niagara and then sail to Ft. Miami (St Joe) with ship-rigging supplies and equipment. At Ft. Crevecoeur (south of Peoria) in February 1680 he decided that he himself had to return to Ft. Miami, and if the Griffon was not there, to go on to Niagara. Of course we know that the Griffon disappeared after leaving Green Bay, never to be seen again.
He started upriver on the Illinois on the first of March, 1680. They ran into ice and eventually abandoned their canoes about where Joliet is now and walked and waded though slush until they got to Lake Michigan. They hit the beach probably about where Gary is now and then followed the beach up to the mouth of the St. Joseph River, arriving at his fort on March 24. The Griffon was not there and he learned from the men left at the fort that it had never arrived at Niagara.
So, when the Heward party paddled down the lake shore south of St. Joe in May of 1790 they were going backwards not only on LaSalle's 1679 eastward and northward water trail they were also going backwards on his 1680 beach walk. Further, when they were wind bound on May 4 through May 7 they literally camped in LaSalle's tracks. I'm guessing that would have been about where Warren Dunes Sate Park is now.
LaSalle was determined to get back to Niagara but he had no ship and canoeing up through Lake Michigan to the Straits and then down Lake Huron would take too long so he decided to walk to Lake Erie.
LaSalle's party for the cross-peninsula hike consisted of himself, four other Frenchmen and a Mohegan Indian hunter/scout. The Indian was not a guide because he was from Massachusertts thus didn't know any more about the Great Lakes country than LaSalle.
On March 25 they built a raft and crossed the flooded St. Joseph River (which they called River of the Miamis). Then they headed up the valley of the Paw Paw River, a tributary of the St. Joseph, following its left bank. LaSalle said that for the next two and a half days they struggled through brambles and briars. (When they were following the Paw Paw eastward between present day Coloma and Watervliet if they had looked across the river through the leafless trees at a particular place on the north side they could have seen the 15 acres where I was to be born and grow up).
On March 28 they came to "more open woods" (Grand Prairie west of Kalamazoo). The sound of their shooting game for food attracted Pottawatomie Indians who were scared off by being fooled into thinking LaSalle's little group was an Iroquois war party.
LaSalle's letter doesn't mention the Kalamazoo River but that is what they would have to cross next. There was a good ford where Kalamazoo is now but they wouldn't have taken it since they were deliberately avoiding Indian trails for fear of Iroquois war parties. Thus they must have crossed the river well to the north beyond a huge tamarack swamp that lay on the west bank.(I'm guessing they constructed another raft to make the crossing).Then they were in a big prairie (Gull Prairie, the largest in Michigan) and set the grass on fire to cover their tracks.
The navigation technology of the time allowed travelers to know their latitude (how far north or south) but not their longitude (how far east or west). Thus LaSalle knew the direction to the Detroit River and Lake Erie but not how far they had to go. So he set a course straight east and they continued walking and burning the grass behind them. This course took them between Gull Lake and the northernmost bend of the Kalamazoo River until they ran into marshes northeast of present-day Battle Creek on March 30.
For the next three days they had to wade through wetlands leaving easy-to-follow tracks. The Iroquois ruse (drawing Iroquois signs on trees with charcoal) which scared off the Pottawatomies got them in trouble because they were being followed by a Mascouten Indian war party which was hunting Iroquois.