I haven't worked on the 4l30e, but I've done a few autos. You can usually improvise a tool to compress the spring plate. I've used a press, or even a drill press and scrap pipe/metal whatever is on hand to compress springs in autos. Sometimes you can even do them by hand, depending on the model.
After reading through the instructions it doesn't look like it would be a problem with a press (drill press will work here, not running of course, not that much tension on the springs). The instructions even mention using the special tools or a press. Possibly it might be able to be done with a friend pushing down while you remove the snap ring.
Make sure your work area is spotless. Thoroughly clean the exterior of the trans before starting. Just a little bit of dirt in the wrong spot will screw it up.