I wonder if it would be possible to use a bar with a tapered end instead of the dial indicator. Manipulate the cross-slide so the point stays in contact with the template. That way, you couldn't go in too deep. It would also partly remove some of the inaccuracies which would arise if the dial indicator had a rounded end, so that on the rounded parts of the template, its contact would be on the side of its end, rather than at the tip. With a finely tapered bar, this would not happen, except where the curves on the template were getting close to perpendicular to the spindle axis.
Just a thought, and it may be impractical. .
Andy.