How to remove/cut off a steel post in concrete
In the end I hired someone to do the work, and was glad that I did.
In order to remove the posts they used:

A reciprocating saw to cut the posts off
An angle grinder to cut more of the posts off
A powered chisel thing to get rid of some of the concrete that was inside the posts
A hammer and lots of effort to fold the remaining parts of the posts down

Here's an image of the aftermath, for one of the posts. (the secondary circle cut in the concrete was there already, and not part of the removal works)