After more gentle nudgings these past days, and generous application of treats, and the addition of one more "stair step", the little cat seems to slowly consider using the board. (The additional "stair step" is a wood ridge right at the bottom, because otherwise her hind paws slip when she tries to step up.) She actually put her front paws up on it today without prompting, then looked about a little, then stepped down again.
Some more nudging, placing her front end on the board again, and then providing another treat did see her up the stairs and onto her cat bed, where she's now sleeping. (Someone has to, after all. Cat beds are there to be used.) Even more importantly, she wasn't rushing up the board trying to get off that weird thing as quickly as possible, but more or less strolling up it.
So it's actually looking like maybe another week or so will see her using the stairs without a prompt - unless she feels like jumping... which may always be the case. I'm fine with her jumping, I'd just like her to have the option of getting onto the bed or desk without it for those days when jumping so high is too hard.