Allow drawing on the "preview" space and translate to the "sketch" side
Especially when trying to draw some straight edges, it might make sense to align the stroke to the center of the view and set the rotation, then using a ruler tool, draw a straight line. The straight line in the preview should then show up as curved on the sketch side. This will help improve precision and alignment when perspective isn't the challenge.
This sounds good! My idea was to adapt the ruler tool so that it snaps to the curved guide lines, or otherwise bends dynamically to produce straight lines in the preview. Drawing directly on the preview with the existing straight ruler could be a more flexible solution.