Welcome to the Forum, your Design looks great
If your Spline could be replaced by a segment of a Circle you could use:
Tools > Rotate around axis to copy and move them.
Transform > Move/Copy > Place the Centre of the this tool on the axis > Tap the Copy Icon and move them.
To ensure accurate placement, but personally I do not think it will look as good as your achievement.
Looking at your Design suggests that the upper portion of the Spline has less of a curve than the lower portion?
To force a Union you could create a ‘modification’ something like this:
Whatever projection you choose will need to be set back from the visible edge face, not to give the game away.
IMO your tiling is ‘perfect’, show me a picture of a similar roof that is aligned as accurately.
Imperfections in this instance may enhance rather than detract from the overall effect?
Keep up the good work, happy S3Ding