I have a 20 year old that went his own way, wont go into details, but there are way way weirder things that your son could be getting into besides Air Force skydiving. I think it would be wise of you to be supportive of him exploring different interests. The relationship that you are developing with him is more important than anything else right now.

If he isn't wanting to serve a mission then continuing to push that is going to hurt your relationship. He's a lifelong member of the Church, he knows what you want as far as mission goes. Have you considered that his anxiety and depression issues may be a result of his testimony not measuring up to expectations? At some point you have let him become who he is going to become. If you can do that and still be there and support him even if he chooses differently than what you were hoping, you are good father.