Firstly, this may just be my inner Scholasticism coming out, but I think that judging the truth of something based off of the emotional affects it has on people is very stupid to be quite frank. Feelings and emotions can lie. They are temporary. They constantly change. They won't tell you what is true, but will rather just tell you how something makes you feel. Reason is the best tool to judge things by because it will not lie to you and will stay true no matter how you are feeling--it is self-evident and objective. Secondly, I think that we need to make a distinction between the types of "Joys" involved. I feel more than qualified to speak on this since I've spent the majority of my pre-conversion life in Evangelical "Born-Again" crowds. From what I have observed, the joy that they experience honestly seems quite shallow and immature--just rooted in hyper-emotionalism. The reason for this is that it constantly needs to be fed. Instead of living a godly life and doing what God says, they spend more of their time trying to satisfy this hunger inside of them for more "joy" and oftentimes go to desperate means to do so. Many Evangelical Mega-Churches have been built because of this. And eventually, what they find out is that this need for "joy" can never be fully satisfied by the world, and they oftentimes see this as being extremely bad, don't know how to deal with pain or accept spiritual maturity, and in the worst case scenerio, despair and end up leaving Christianity altogether.
This is the joy of the demons. It is built upon hyper-emotionalism, leads people into despairing and blinds their eyes to true spiritual development and joy. True joy is not about feeling no pain or sadness--indeed, Jesus specifically tells us that we will suffer for Him constantly--but about accepting our struggles and sorrows in a submissive manner, learning from them, and even reflecting on them to learn how we could glorify God through them, and most of all, staying submitted to God throughout it all and thanking Him.
True joy produces humility and humbleness--and that brings me up to my next criticism of Evangelical "joy". I find that the Evangelical sense of pride oftentimes leads to a not-so-subtle sense of pridefulness and individualism. Many Evangelicals I've met who've matched your description of possessing that sense of Evangelical "joy" oftentimes begin to think that they do not need Church at all or any guidance from their fellow Christians because they see themselves as having their own special line with God and capable of working out their salvation on their own. This is the joy of the demons--subtle pride, a rejection of the Truth, blindness to true spiritual development, eventual despair etc. I wouldn't touch this joy with a forty foot pole.
Now, the true sense of joy--something I admittedly don't have yet--I observe among several of the older folks at my Orthodox Church who come from troubled countries and are close to dying. These people seem to be emotionally dying and full of troubles, yet, in a strange way, they have not despaired but have accepted their tribulations and offer them to God. Instead of trying to escape them with this shallow sense of happiness that constantly needs to be fed, they face them, learn from them, and come closer to God through them. Their sense of true joy doesn't cause them to become prideful or to leave the CHurch, but rather causes them to be extremely meek, quiet and humble, and come to the Church more often than anyone else. They truly seem content with their life, knowing that they need God more than ever and that there are things wrong in the world, but submissively handling them and turning to God. This is the true joy--the joy that I hope to attain. It is not shallow and prideful, but deep, beneficial for learning and produces humility and submissiveness to the Truth and Church.
Any sense of "joy" that produces pride and not humility and does not lead a person to the Church is the joy of the demons.