Ford loves weird things, so obviously he loves the ocean and aquatic environments. Even the "non-Weird" species are SO weird--- see-through fish, blue-blooded arthropods, things with no eyes or too many eyes or eyes radically different from ours. So when he goes to Backupsmore, his focus ends up not just in physics but in aquatic biology--- not marine science, his true love, because the ocean reminds him too much of his brother, and the Stan o' War, and a dream that was never meant to be--- but freshwater is... similar. And strange. And some lakes here in the continental U.S. are as big as saltwater bays and seas, and just as deep, too.
So instead of Gravity Falls, Oregon, settled into an old logging forest, he finds himself in Gravity Falls, Michigan, on the isthmus between Lakes Superior and Michigan. Midwesterners are too nice to say anything about his hands or past or odd habits, and the lakes are huge and packed with Weird creatures--- monsters that would put Loch Ness's own to shame, loons made out of lichen, dragonflies the size of his arm that whisper the future in the beat of their wings. Just being by the lake isn't enough for Ford; when he builds his lab, he builds it on the water. He builds a lab-boat.
Perhaps the portal is constructed on a small, otherwise unnotable island on one of the lakes. Perhaps Ford builds a submarine and constructs it under the water, where its form is tangled with sea grass and its swarmed with fishes both typical and unusual. But Bill still gets into his head, the portal is still constructed, he still calls Stan for help, and he still gets pushed into the portal.
All of this to say: the Mystery Shack as a traveling houseboat in the Great Lakes system. Stan on a boat, but a lake boat representative of his deepest failure as a brother; Stan who constructs the weirdest, cheesiest, most environmentally concerning barely-floating structure that draws in the locals on their speedboats and tourists who pay local captains to take them out to the bobbing monstrosity. Stan who paddles to a different lake when he gets in trouble with local law. Stan who, when he's in the middle of Superior on the Canada-US border, when it's dark and he can't see land, when the wind makes rolling waves he can almost pretend are flavored with salt, can imagine, for a moment, what life would've been if only he and Ford were on the Stan o' War. It's what he dreams of as he works on the portal with the late-afternoon duck calls echoing around him, his only company the birds and the bugs and the fishes. At least, before Dipper and Mabel show up.