The results you got from the on line calculator are very close to the results I get with a field solver.
Your options to reduce the trace width are to reduce the thickness of the board, or run a return ground path in parallel with the top trace. The spacing of the ground path would be adjusted to give you the desired impedance with the desired trace width. This, of course, means two traces where you would have normally placed one.
Another option is similar, but the structure is different - you run your signal as a coplanar waveguide. To do this you run your signal down the center of a ground plane on the same layer (in your case the top) by making a slot of the proper width in the copper pour. The disadvantage to this method is the loss of space on the top of the board for other components because of the ground pour.
Reduced board thickness, or the use of internal planes with thinner dielectric between the signal and the return path is the most efficient if you have many components. Differential routing, using two traces (one is the ground return), is the simplest way to do what you want with only two layers and the same board thickness. The coplanar waveguide is the cleanest from a signal integrity standpoint, but uses more space on the top of the board. You will have to chose which compromise gives you the best solution for your particular board.