oh. one of those.
yeah, you can't do it solely with standard sketchup inferencing.
i bet there are quite a few tricks out there but my own go to is similar to yours except i'd use TIG's extrude edge by vector to make the vertical face.. (select a line, extrude it up (or down) but keep it as a group for easy deletion when your done with it.. draw the vertical line then delete the group).
i guess if i had a lot of these on one drawing, i'd consider draping all the criss-cross lines (sandbox tools) onto a flat plane which would show you where the intersections are.