You're doing it the right way. If you push the release button as on pic #12 in Ajoe's tutorial and pull the stem it is supposed to get out. Maybe you need to put the pressure a little bit up and use tweezers instead of a plastic tool. It's not as fragile as a 2824/36. The pusher can handle some force. But don't overdo it off course.
As long as you don't dissassemble the whole movement you don't need to release the spring.
The more difficult part is getting it back without damaging the keyless works. You need to press the release button and at the same time slowly put the stem back while 'winding' the stem anti-clockwise. When you feel the stem engage you can press it further in and keep pressing the button until the stem is full in. If you don't feel it engage start over again, because you can mess everything up when pushing it in further.
Also be careful with taking the 3717 dial off, since most of the time the black paint can easily fall off just by touching it on the edges...
If you don't feel comfortable with this you'd better send the whole watchhead to your AR guy and have him release the movement and get the crystal out. I know K2222 does that. I'm not sure with Chief, though.