It takes a little practice but you should not be trying to crop the image out. You just remove the color and it leaves the background transparent. There are a couple of other settings that you can use. I do this all the time and can even get hair to show correctly so you see the hair and the new background behind it.
The refine edge tool will take care of that halo around the edges and also the hair. It does take a little practice. But Green screen software is generally cheap and does not do as good a job as what you are already doing. A little practice and you will get it.
Just learn how to make a "Selection" and once that is done you can put your subject on any background you wish. Learning some basic Photoshop skills will help you a lot more long term. If you are not familiar with how to use the selection and refine edge tools search on youtube for tutorials.