In Vim I would enter visual mode with V then just move the cursor up (with k).
In kak I can select a line with x and I can extend the selection downwards by pressing X multiple times or by moving the cursor down while still pressing shift with J, but if I go up while still pressing shift, with K I keep the selection, but not for the entire line, the selection on the first selected line somehow jumps to column 0.
It's not ideal, but at this point the best I can find to make full-line selections up is to do what you've described: x and then scroll up by pressing shiftk.
Only once you've finished scrolling up, you must then expand the selection to include all full lines by pressing altx.
See the discussion in this Github kakoune issue for some great scripting solutions to this problem that you can add to your
kakrc
.One of those solutions is featured on the kakoune wiki: