It's great that you understand grain direction and how it runs opposite on the other edge of a board. You didn't say what type of profile you are cutting. Most router cuts are better done with incremental cuts rather than one cut set to full depth. That may not be enough when cutting against the grain, particularly with species like oak that tends to splinter and tear. With some profiles, like a chamfer or roundover, you can often over come the wrong grain direction by running the board up on edge, rather than flat on the table, so it cuts with the grain. The bit has to eventually be set so it cuts the same from the face and the edge. In woodworking, when a cut is not coming out smooth or it's straining the tooling, it's always best to slow down your feed rate and take less of a cut. Slowing down the router speed is contradictory, slow your feed not the bit, unless you are running a large bit that requires a lower speed, anyway.
Another technique is called climb cutting. You run the lumber with the rotation of the router bit, not against it. This can be very dangerous since the bit wants to grab the work out of your hands and throw it across the shop, blink of your eye quickly. It's not easily done on a router table but can be done with a bit more control with hand routing. Incremental cuts in a hand held router can be done with a fence attached to the router along with setting the depth of the cut. It can be done on a router table with use of a strong stock feeder, but still with incremental cuts.
Nibbling is another climb cutting technique. Instead of starting on one end and feeding the stock from that end to the other, the way you ordinarily do, you start at the far end. Like making a stop cut, where the profile doesn't go to the end of a board but stops. You "drop" the work on the bit. In nibbling, you drop in close to the end and feed with the bit rotation just a small amount, maybe 1" or less to the end of the stock, depending on the profile, etc. you then move ahead another 1" or so and repeat, moving toward the area you just removed. This eliminates uncut stock behind the bits rotation, which is what causes pieces to be thrown. When shaping edges of curves, the grain always runs opposite each side of the apex. The nibbling technique is commonly used for the side of the curve that has grain running the wrong way for a forward pass. An arch top door or window is a good example.
A sharp bit is necessary for a good cut. Making a zero clearance hole in your fence for the bit can help with tear out since there isn't a large enough opening for splinters to be pulled into. The combination of these techniques is your best chance for a quality cut that won't need additional sanding, it's not always fool proof but it's the best you can do with a router.
