I recently embarked on the same journey as the OP, looking for an app/program that would I could use to keep all my songs listed with access to words, music (chords, tab, etc) and other features. I ended up going in a completely different direction after stumbling onto an app for a website I had already been using for years. It will do most of the things on your list.
I no longer even bother to keep the cards I used to keep for every song. Instead I have a master set list and then I keep a separate list of edited songs that display just the chord progression. Since I'm not the singer that's all I really need. That list is only for the newer songs that I have not quite as yet mastered.
Might be worth checking out. In my case, what I thought I needed and what I actually needed ended up being two completely different things.
I did a complete write up on it here:
Guitar app (Android) review: Ultimate Guitar: Chords & Tabs