Haven't read through the whole thread, but did do a quick search for the word "sulfur" and only found one comment regarding high pH soil and adding it...so I think it's safe to assume no one hit on this secret tactic. I've used it myself and it's been working miracles for me on my tight clay soil (and I've found 15 year old saplings, fir needles and goldenrod buried in 6 inches of clay that haven't rotted one bit!)
Soil science is key to understanding the behavior of things like clay and it's ability to be one of the best bases for your soil, or one of the worst.
Many people immediately think of gypsum for clay, and this is because the sulfur in the clay will help "deflocculate" or break up the clay. The presence of calcium is also great, helping to balance out the pH of your amendment. It's smart thinking, but there's more to the story.
The reason that sulfur helps "break up" clay soils is there's a tendency for clay, composed of tiny flat plates, to hold on to all sorts of positively charged ions. These are generally known as cations, and include most of the things we know our soils need for healthy plants (calcium, potassium, magnesium, and so on).
Clay is awesome in this respect, but can create a major problem. When two plates of clay attach themselves tightly to one magnesium ion, that magnesium ion basically acts like glue between them. Magnesium is a large ion compared to many other cations we want in our soils like calcium and potassium, and they often become trapped between those glued together plates. Suddenly, we have a tight packed clay with no available nutrients. This doesn't allow water to penetrate properly, resists the growth of plant roots and fungal networks, and eventually excludes most soil life, leaving you with a dead mineral soil containing no organic matter.
Sulfur is the magic bullet, chemically binding to the magnesium, "un-gluing" the clay plates and releasing all the other cations. A soil that tests acid before application of sulfur will often begin testing more balanced a year or so after a good application of elemental sulfur. It seems counter-intuitive because sulfur makes soil "acid", but the release of those other cations often makes up for that all on its own! This is why applying gypsum is often the go-to for people trying to improve clay soil - the gypsum contains some calcium and a whole bunch of sulfur.
It's expensive, though...more expensive than a big sack of elemental sulfur with subsequent application of hi-cal lime later if you find you need it.
Oh, and all this soil science brings up another important point. It's pretty much never a good idea to add magnesium if you have tight clay soil - that will likely make things worse. This includes epsom salt (magnesium + sulfur).
So my recommendation is to start with first making the clay behave - add elemental sulfur this spring when the ground warms up enough for dandelions to bloom (probably mid to late may there). It'll likely come in a 40 or 50 pound bag of little yellow "buttons". These break down into sulfuric acid in the presence of water at the right temperature (above I think 50* - don't quote me on that), leach down into the soil and subsoil, and gobble up magnesium ions that are gluing your clay up tight.
Give that about a month to work, then add a heavy dose of kelp meal, feathers and bone char, or whatever sort of organic type amendments you like to the sections you want to garden in. Sheet mulch directly over this (cardboard or newspaper covered with a good layer of mulch hay or clean straw), then give that another month and a half or two months to sit. Note that I have not recommended digging AT ALL yet. Let chemistry do that part for you at this point 
This should bring you up to around late July to mid August somewhere, which is perfect timing to pop in some of your favorite brassica transplants for late-fall harvest! This is about when I'd be putting in the final broccolis, kales and seeded in turnips here in Central Maine.
Spring of 2024, you should be set to throw in some potatoes and use that as your excuse to "till" a little Be sure from this point forward to keep that soil covered at all times with everything you can think of - mulches, cover crops, chunks of wood, rock piles to give the garter snakes a place to hole up, and the best polycultures you can come up with. The improvement of your soil should be much faster by using sulfur early. Also, by not digging / tilling anything until after the chemical magic has taken place, you'll be less likely to turn the "garden" into something like a cement pad where what should be turning into beautiful organic matter for your soil instead gets preserved for future archaeologists 
Oh! One more thing: Make sure any straw, hay or manure you use is not contaminated with the aminopyralid herbicides being used all over the country right now. A farmer would know it as Graze-On. Presence of that in anything you put down will ensure you wont be growing a garden there for the next 5 to 7 years as it'll kill everything but grass. Evil stuff 
