Imagemagick is fairly versatile and I haven't come across any other tool that is close to the capabilities of imagemagick. The tool is fine, the problem might be with what you are trying to do with it.
Since I do not have the image which you are using I have used an PNG image of my own. Two possible problems I see with information you have provided.
The resize arguments you have given are absolute and very large (14384x49152). This means the convert command will return an image of smaller size only if your input image has a resolution greater than 14384x49152. I'm not sure what you case you have for such a large resolution, but if you are going to increase the resolution then correspondingly the size will also increase. And since most images are smaller than 14384x49152 your command will almost always output and image of bigger size than your input.
Your output image is again in a PNG format, which is a lossless format. If you do not strictly need PNG's use a lossy format like JPEG will allow you to control the quality and hence the size of the image. Then renaming the extension to jpeg in the convert command would give you a significant reduction straight away.