I too prefer just PS1='$ ', I want the cursor to be the same distance from the margin every time, to have maximum length for typing without wrapping, and the ability to put in a few separator lines between command output by just tapping Return.
However, for your problem, have you considered the terminal's title instead of the top line of the tty? printf '\033]0;foo\007'
Mine has a bunch of info, then a newline, then ' $'. Being able to see the current git branch is just too useful to drop, but I moving random distances out from the margin between commands.
No, I meant the window's furniture so no colours. I agree, a tty-wrapper, like tmux, would provide another option. I don't suppose there are terminals generally about where `tput hs' is true. Have you considered using the end of the prompt line for status, returning to the left for the "$ ", and being happy to do readline's redraw-current-line if you don't like the overwrite should you reach that far?
However, for your problem, have you considered the terminal's title instead of the top line of the tty? printf '\033]0;foo\007'