Yo. Just finished my first readthrough of the series, started the audiobooks for my second readthrough. Came up with a bunch of theories, some of which I didn't see discussed anywhere here. The meatiest of them is this:

Demonreach the Island can move, or exists in multiple places in space as well as time.
I base this primarily off of the topography and geographical conditions that formed Lake Michigan, what I see as hints from JB, and inferences based on how we know the island's prison works.

Geography:
The closest natural "islands" to Chicago are Marina Island in St. Joseph, and Harbor Island in Grand Haven, both all the way over in Michigan 60 miles and more than 200 miles away respectively. On top of that, neither are proper islands on the lakes, they're points where rivers leading into the lake split and pour out into the lake with land in between, formed by rivers, not the glacier action that made the lake itself. Point being that there are just no "out in the lake" islands anywhere near Chicago (I know the text acknowledges this, but when JB ignores a basic physical law of reality such as how islands form, he tends to come up with a way to justify it). This is because the great lakes were formed by glaciers scraping over plains, which doesn't leave much room for big rocky outcrops that would eventually stick up above the lake's water level. The north part of Lake Michigan has plenty of islands, but zero proper natural islands in the south. On top of that, if you look at pictures of islands in the great lakes, especially the lakes in northern lake Michigan, you'll notice that they mostly all have a pretty similar look: low, earthen islands with gently sloping hills, dense tree cover, and they rarely ever reach more than 50 feet above water level. There are no high rocky hills towering over the landscape, that's more of a UK thing, *cough*.

There was a much shorter, easier way, down what looked like a sheer rock wall. It proved to have an ancient narrow gully worn into the stone, almost completely hidden by brush.
This is odd for an island supposedly formed in the great lakes, since the vast majority of them are essentially big piles of silt and dirt deposited on a high spot in the lake bed, not rock outcroppings pushing up.

From turn coat. "Sheer rock" cliff in a region where islands are big silt piles covered in trees.
Hints:

"Doomed warrior,"... Excalibur

If we assume the island can appear and disappear or exists in multiple places there is an Island of Apples in British mythology, one explicitly connected to Excalibur and the fae folk. An island to which a warrior who wielded Excalibur was taken away, to be kept on the brink of death, until he returns in their time of greatest need... Thomas? Freezer boy? Morgan? Michael already DID return. I mean seriously, the island were Excalibur is kept is explicitly connected with apples, doomed warriors and fae sorceresses? I felt dumb for not noticing the connection in TC when SG rolled around and JB hit us with a clue bat by sticking Excalibur on the island. Weird how much Harry is starting to parallel IRL Merlin myths, but that's been discussed at length.

As a side note, If Harry ever eats one of those apples and notes it to be oddly bland and bitter, we'll know they're heritage breeds of apples from an older age, before we made the big juicy sweet ones we have now by selectively breeding them over the past millennia or so. Apparently old-school apples were comparatively bitter and dry, which is why they were primarily used as stew vegetables or fermented into cider, rather than being eaten on their own. "Like a somewhat sweet potato".

So I thought about hornet’s nests, and instantly felt certain that there were thirty-two of them spread around the hundred and fifty or so acres of the island, and that they were especially thick near the grove of apple trees on the island’s northern side.

This is noteworthy because apple trees are not native to North America. Since there was a town there, it's entirely possible the would-be settlers planted a grove, but to me this seems unlikely since the soil on any small islands, and midwestern islands (re: big silt piles miles from a river) in general aren't great for agriculture, so it seems odd to spend the time and labor to plant a whole grove near an island town that would have been a waystation with few if any permeant residents.

There were deer on the island, though God knows how they got there.

I think this might be Jim trying to give a hint that there are more ways than "swim from chicago" to get to the island, whilst kinda showing a lack of knowledge about wildlife. Ungulates being present on islands many miles away from a mainland isn't strange at all. They can and do swim for many, MANY miles. This could be Harry's lack of knowledge, but since he's the tracker, "knows all the birds' names" Strider type, I'm guessing it's Jim. Overall I'd say it was meant as a hint.

How the island works:
To pull all this together, I'd point out the obvious and ridiculous tactical weakness of a static island in lake Michigan: you have to get big beasties from all over the world to a static island in lake Michigan. Even with the reveal in BG that you can work the binding from the shores of the lake, that only takes your local-use-only superweapon to a regional-use-only superweapon. I'm aware of the big summoning circle by the lighthouse, but think of the practicality of using it. We know from the Azothrogal summoning sequence in GP that summoning even a bog-standard demon can be quite a struggle. Yes, harry was a young puppy of a wizard, working with average tools, but I still think that the process of forcing a god or titan to respond to your summons, and then going through the psychic wrestling match of binding it would be too much for any mortal wizard. Demonreach didn't help with the spiritual struggle part of the binding, only with the locking up once Harry had won, so there's no reason to assume he'd help with the summons.

Further Speculation:
This whole situation starts to make way more sense if you can teleport the island to any body of water, or even to a number of fixed points. Five places in space, for 5 places in time, perhaps? Maybe it just exists in all 5 places at the same time, and Harry hasn't yet realized he can leave through any of them. I'm only aware of a couple of disappearing islands in mythology, but if we can lock down a few of them that could have connections with mythology addressed in the Dresden Files, you could narrow it down. Lake Michigan is one. Avalon somewhere around Britain would be another obvious one, what with the Excalibur, faerie queens, and repeated "doomed warrior" connections? Didn't Calypso or Medea have an island that could only be found once? That would cover the Mediterranean. Since the Japanese have approximately 250 million folk myths, I'd be shocked if they didn't have a moving island, which could cover east Asia. Makes me wish I'd read more mythology.

Apologies for the dodgy formatting, it's been a minute since I used a proper forum.