Keynav is good but warpd [1] offers all of keynav's features and more (and on Windows, an equivalent of warpd is mousemaster [2]). They not only implement dichotomic splitting but the hint grid too. And they're both FOSS software as well.
Ok so just a warpd/keynav style grid mode then? I thought OP was describing a novel concept based on the idea that initially the whole keyboard would represent the entire screen.
I don't get the last part where you repeatedly have smaller and smaller rectangles, can you expand on that? How are the rectangles defined? I pressed H, I'm at the center of the screen. Now what?
[1] https://github.com/rvaiya/warpd
[2] https://github.com/petoncle/mousemaster