A large drill might be a beginning and then chisel.

The only other suggestion I have is to drive two flat steel plates on either side of the wood, long enough to reach the dirt bottom and be above the ground.
Then bolt those plates through the new metal posts connecting both plates.

Typically the wood rots right at surface level, not above or below.Concrete adheres to the wood like glue and makes it nearly impossible to pull out.

Rent a HD drill with a 1/2″ chuck and one or two 24″ wood bits of ~1/2 to 3/4″ diameter. Drilling the first hole in the center of the post, carry on with as many holes as you can, as close together as possible without running them together, straight down through the bottom of what is left of the wood post. Once drilled, use a chisel to break out the middle of the wood first and work your way out, chiseling or prying towards the opening you created in the center. With a little luck the entire section of broken post can be removed this way, but if not, don’t sweat it.

Once you have enough wood out to at least start your metal post, you should be able to pound it in the rest of the way, as the remaining holes will collapse somewhat to allow entry of the post.

When the post is in place, fill around it with a special, extra strong cement mixture such as “Set 50″ or “Set 80,” tamping or vibrating to fill voids and remove air bubbles.

Use a drill and chisel. Spend a few days at it and that might work. You could rent a concrete saw and cut around the areas, then but out a smaller amount of concrete along with the post ends. Or, you could try using a method for removing stumps~ douse the posts in fuel oil, let it soak for a few days, then light it.

MOVE THE NEW POST 1 FOOT AWAY

i would drill as big a hole down through the wood as i could and then take a sawz-all and clean the rest of the wood out…drive your metal posts into the ground and use non-shrink grout to anchor them…