If I'm reading correctly what you're trying to achieve......
Your cardboard template won't be perfect when you put it in, so use a spacer (aka scribing block) at least as high as the widest gap between your keel and your cardboard. Lay the spacer (small piece of wood or something) on the bottom of the boat 1/4 inch or so from the transom, lay a pen or pencil on top of the spacer with the point touching the cardboard transom template, then drag both the pen and the spacer together as a single unit along the keel and the line you draw on the cardboard will replicate almost exactly the contour of the keel as your spacer is always touching the keel as you drag the unit. Then cut your cardboard along that line, and use it as a template and you'll have transom wood that perfectly replicates the contours of your keel.
Here's a picture example of scribing. Difference for you is that your wood scribing block will be a smaller piece, unlike this picture which is a simple straight line along the full door. Yours will allow you to follow contours as you scribe your line.
http://www.truvalu.net/images/Projects_T-Z/130scribe10.gif