You probably need 2 bits to do this and they both probably need to be 2", you may be able to get away with 1.5". The thing you do not seem to be accounting for is clearance above the cutter. If you start with a flush trim bit and the pattern on the opposite side of the workpiece, the rough cut stock would interfere with the shank of the bit, preventing you from following the pattern. If the cutter diameter is enough larger than the shank diameter, you could use it, but the total length of the cutter and the exposed shank would need to be at least 3.5" just to reach the pattern. Keep in mind that the bit would have to be more like 4.5"-5" to have enough length to cover the full workpiece and have enough shank to mount it in the router. The pattern bit would have the same problem (except since the pattern is at the top, no issues with shank to rough cut wood interference).
So, the way to do it would be to use a pattern bit for the first pass(es), and use a flush trim from the opposite side for the final pass. This prevents you from having to get one bit to stretch across the entire workpiece. Another option, would be to mount a spindle sander drum into your drill press and sand to the final shape. (Just don't try to mount a spindle sander drum in your router table, the speeds are too high.)
(Note that when I reference top, it is based on free hand router operation, even though you plan to do this in a table.)