Here's an option, put a 2x4 flat in the bottom of the wire cage in the middle, she can stand or sit on that to rest her feet from the wire. It shouldn't hold TOO much heat against her belly to keep her broody and it may feel enough like a perch that she will be "perching" rather than "brooding". Supply unlimited food and water in the cage so she can eat and drink. It may not be quite as effective as having her straight on the wire, but it should ease your worries about her comfort as she isn't being forced to be on the wire, she can get on the board at any time she wants off the wire, same logic as your ice packs.
Honestly, from your descriptions, you seem to have 2 options, make her slightly uncomfortable for a while by putting her in a cage to break her, or let her be "happy" and watch her starve herself to death in the nest.
Something you don't seem to have considered as well is that some broody hens will not take grafted chicks, so even if you get her young chicks, she may freak out, kill them, and continue her broody streak... No, it's not logical, but she's a hormonal bird brain, you can't really expect too much out of her....