I was about to reply and say that I could run FRED under wine but I couldn't save anything. However, I thought I should just try again (3.6.14 RC6 FRED - latest version I have hanging around) and saving worked just fine!

This was a clean WINEPREFIX (WinXP mode), wine-1.5.14 on Mint13 x86_64. Note however that I haven't done anything except add 4x Hercs, create two wings Alpha & Beta, then saved the mission so it's not exactly a good test...
And - just noticed that you're asking about Diaspora, not FSO. Oops. I don't have the Diaspora Windows FRED exec on my PC and a couple of GB download just to get it from the installer seems a little excessive, but it may work OK as I described for FSO above. If you want to post your Diaspora FRED exec, I could give that a go and report back...