I got a chuckle, because we are so similar, but backwards! I set the grade zero, and then think, "OK that's the basic exposure, now let's set the contrast right". I have not tried it your way so I cannot have any opinion about which is better. I also like a very short burn of the sky with high contrast... it brings out the edges of cloud shades, just as you say. I burn and dodge with the low contrast exposure too. I like how it is possible to pay attention to different parts of the picture and vary local contrast.
It's been 30 years since I printed before, but I do have a memory of getting frustrated juggling graded paper contrast and exposure. I like split grade printing too, even though I fell into it more out of necessity if I want to use VC paper. ( My understanding is that the normal VC filters have uneven steps and are hard to use with my enlarger. ) There's a certain kind of logic to it that I find appealing.