Looks good. Seems like you're able to do most of what you were asking for and this is a good base for similar problems.
I believe there are commands for placing slider bars in the description of geogebra's JS interface. You can construct a <script> </script> segment that creates these codes in webwork and then print that to the webwork page using TEXT() to create the objects dynamically.
I'm at the joint math meetings (JMM) at the moment . I'll be back in Rochester next Monday