ImgBurn was able to see there were multiple sessions on the disc, but couldn't access them. It was able to burn an image of the disc (presumably including the sessions), though.
I downloaded Nero 2014, which had a 15 day trial. It had a "Save Data Track" function, which seemed like it was meant to extract data from different tracks, but it could only select the first (oldest) track.
So here's how to do it (for free). It's a bit of a roundabout way, and not very efficient. Troublesome if you have several sessions to extract from. How it works is I burned a new session linking to the session I wanted, then copied data from that. I think it should work for CD-Rs too.
Requirements: Install Nero 2014
- (Not necessary) If your data is important, make a copy of the disc and work on that.
- Start Nero 2014. In the Multisession tab, choose "Continue Multisession disc".
- It will ask you to Select Track. Choose the session you want.
- Now you'll be able to see your files from that session, but there doesn't seem to be a way to copy them out. Just burn your current, new session. What this does is create a new session with links to the files in the older session, without adding any new files. Nero can't burn this as an image; you have to actually add a new session to the CD-RW.
- After burning, you can insert the CD-RW and directly read that session.
- Repeat for any other sessions you want data from.