Hahahahaha! You sound appropriately enthusiastic! Hooray for the demise of the decking!
I would also buy a large mattock to go with that demolition bar. They are the accessories of the season on this forum, for a very good reason. I imagine if you dig around the posts with one of those, it will be a quicker job that with a spade. You will also feel like Buffy wielding one of them.
Why is it that the things you don't want are always utterly solid?!
Yep, dig down with a spade (or mattock, if the earth is rock hard and dry), uncover the concrete, and then you can lever it out with the pointy end. The concrete will just be a big plug of stuff that can sometimes be lifted out in one piece with the post, just like a big rock. Sometimes, though, you may need to smash it into pieces (wear glasses!) because it's too heavy to manouevre otherwise. This is great fun, though hard work when it is hot.
If the post is too much in the way, you can just cut it down.