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The interior hole in the Lee 82mm Wide Angle adapter is the big limiting factor for the approach described in this thread. It has an interior hole size of about 79 mm, and is limited to not being larger because it must provide exterior threads to fit into the inside of 82 mm lens threads. If the interior metal could be removed by machining the 82 mm Wide Angle adapter, the hole could be enlarged, but not by a lot, because the actual Lee filter holder mounting flange is about 89 mm, so you would need to leave a hole of about 88 mm. That is an improvement, but it would require special machining that is not easy.
But the Lee 82mm Wide Angle adapter is actually made from two metal parts, which look like they have been screwed together with thread lock or epoxy to hold them in place. If you could remove the inner metal part that provides the 82mm threads, it would open up the adapter to a hole size of about 86 mm. One possible way to do a removal is to use a small grinding tool and carefully remove one portion of the inner ring. If you can get one short portion removed, the rest may come out easily by prying, because of the gap you have made in the ring. This is similar to cutting the metal of a stuck filter to get the remaining ring out of the lens. In this case, it does not matter if you slightly damage the threads on the outer part, because you are not using them for this project. If cutting one short section out does not work, you can cut out a second section opposite from the first, and then the two parts should be much easier to remove. I must warn that I have not yet tried this, but it looks very practical to me. It is also a much easier do it your self project than machining.
You might think that other Lee adapters that fit larger thread sizes would have larger holes, but they are all limited by what hole you can fit through the standard Lee flange, so you get no more. As an example, the Lee 105mm lens adapter has an interior hole of about 79 mm, so that is actually slightly worse than the 82mm Wide Angle adapter. But if anyone were to consider machining an adapter to enlarge the hole, I would suggest you consider starting with the 105mm adapter, because it has much more metal in the outer part of the ring, which will make it much easier to hold in lathe jaws for machining out the inside. It does have a larger outer diameter, but that could be machined down to just the right outer size to fit the lens cap interface after the inside machining was done. Or you could leave the outer 105mm threads on the adapter, and glue the right step up ring to the lens cap to go from its size up to the 105mm threads.
So the extra 7 mm or 9mm of hole size would help. To get more, you need to go away from the Lee system for providing attachment and rotation. The combination of the Lee adapter with flange and the clip on Lee filter holder is what provides the rotational adjustment for the filters. And that rotation is even more important on a Canon TS-E lens, because the whole lens rotates on the camera to align the tilt and shift axis. One thought I have had in the past to provide rotation is to get a cheap 105mm polarizer, and remove the glass from it, and use it as the part that can rotate. That could give an interior hole of about 100 mm, which would likely be plenty for much larger shift amounts. But you then still need to attach the rotation part to the lens cap. A step up ring from a smaller size up to 105 mm may work to act as a part that could be glued to the lens cap part. Because the glue on location is further back, is can have a smaller inside diameter. The lens cap plastic is about 88 mm inside diameter, so trimming it back as far as possible before increasing the diameter beyond that would be the goal.
For using a 105mm polarizer metal for rotation, you still need to attach the filters to the front of it. The plastic of a Lee holder is one possibility, and it could be glued on to the front of the rotation metal. The hole inside the Lee holder has a diameter of about 96mm if the small fitting tabs were removed by grinding or filing. You could also enlarge the inside by making the hole more square rather than round, with the sides of the hole parallel to the filter holder slot fittings. The removed corners would often be in alignment with the corners of the rectangular image frame for the common use of the graduated neutral density filter alignment near to parallel to the horizon.
Another possible approach to attaching the filter holding slots is to use a different piece of plastic or metal, and attach it to the rotation metal. You would then attach the Lee filter holder edge guides to that alternate material using screws. You could potentially make something that has a square hole that is a full 100 mm or so, and would match the limitation of the 100 mm filters you are using. And if you really want to get carried away, you could design it to work with the even larger filters that the special Lee system uses for the Nikon wide angle zoom lens, but that means new expensive hard to get filters.
Getting the filter slots as close to the front element as possible without danger of touching is very important to provide the least potential of interfering with the image edges. So pay attention to any build up of an adapter system and try to achieve that goal. And if you do something with an enlarged center hole, you may now need to worry about a second filter that is further forward, and could become limiting. Consider only installing one filter slot on the front, rather than two or more. Lee has shorter screws available that can be used for that purpose.