so according to what I am understanding I will need a 3½ inch radius bit, correct? does that even exist?
correct..
the bit, actually a cutter, does exist but that will take a shaper to turn it... not a router..
what you are showing is the face of the 2by and the ends...
the edge is 1½'' thick...
rough cut it to size and sand to final...
an ROS will do it...
as well as a disk, belt or drum sander...
a disk sander will do the best job..
2nd choice is the belt sander...
make the tool stationary and move/rotate the wood over the sanding surface...
all w/ a little practice you'll get what you are looking for...