Why do my English muffins have such a tough crust?
I strongly suspect that it's the trip to the oven that's making those muffins tough.
My personal recipe for sourdough muffins does not involve baking them; they are cooked entirely on the griddle.  I checked three different sourdough muffin recipes (1, 2, 3) and none of them used the oven either.
So my suggestion is that you try cooking them entirely on the stovetop and omit the oven.  This will require longer cooking on the griddle to make sure they're done all the way through; I suggest checking with an instant-read thermometer (should be 90C in the center).  I don't suggest lowering the griddle heat, which should be around 175C ... cooking them longer may actually toughen them.
The second thing I notice is that almost every sourdough recipe I've checked has some kind of fat in it, usually butter or whole milk, and the recipe you linked does not.  The recipe I've tried that doesn't is Arizmendi Bakery's, which are also very chewy and tough to bite into (I like them, but I suspect you wouldn't).  So adding some kind of fat to the recipe would probably help your crust texture; it generally does with bread.
There's other general tips to peruse, just in case you're running afoul of something else like using way too much flour during kneading.
It's also true, though, that different sourdough cultures can result in chewier (or less chewy) crusts.  So if eliminating the oven step and adding fat doesn't work, I'd suggest testing a non-sourdough recipe to see if you're having the same issue there.