I have heard complaints that some carbon fiber frames from about the year 2000 to the year 2010 were considered overly stiff. So that might be something to try, and might be cheaper to experiment with.
You could look at a steel frame with oversized or double oversized tubing. However, they tend to make the tubing thinner with the bigger sizes.
You could talk to a frame builder, and see if they had any suggestions. Perhaps use oversized MTB or touring tubes on a road bike build.
If you do want to stick with carbon fiber, I'd look at some of the cyclocross frames.