Edwin has given you some good information. Backing up the stock is
good. It is similar to usiing a zero clearance insert on the tablesaw.
The block needs to fit tightly against the long grain side of the board
so cut the end grain first.

Climb cutting (feeding from left to right on the router table) can help
but you must be very careful because the router will attempt to pitch
the work across your shop and chew up your fingers.

You also got at least one point. If the profile will remove a bunch of
wood, make the cut in several passes. Move the fence to adjust the
depth of cut.