Hey folks, I've just figured it out!
Well, there's no direct feature for rotating the board in 2D mode, that's not news... But it turned out you can do it, and it's not a huge pain in the ass.
Simply – just select everything using mouse, drag it a little away and press the "space" key.
Whole freaking board rotates by 90 degrees easily. Took me 2 years of laying out PCBs to figure it.
Yeah, of course Altium thinks you've just rotated the components and board shape is still the same.
Well, that can be easily fixed by selecting flipped outline and defining new board shape.
Easy peasy lemon squeezy.