I'm not sure about Fireworks, but over the last couple of years post redesign it has been only jpg that has been off in color when I export it in Photoshop. Because, in PS, you are able to 'save for web' which gives you various options for how exact the palette is and at hat size you need it to be. When I do this, my gifs are exact.
And so my only suggestion is that you try Photoshop if you 'purchased' it along side fireworks in a CS suite because it has these options.
But yeah I am not familiar with Fw.