I did it!
At last, I managed to finish my Impossible Mage game. I used human troops on the first island and the first fight on the second island. Then I switched to a single Emerald Dragon for the 5th fight, which proved very easy, and just 2 Emerald Dragons for the last fight.
The final fight was VERY difficult like this, and took many reloads. Here's how I eventually did it. I had been using Ancient Phoenix as my main attacking weapon (see my combat statistics in that regard

) but I found it not so useful on this last mission as it died too quickly. I was really struggling and thought I might not be able to do it when I found the Peacefulness spell for sale.
So Peacefulness on Emeralds Dragons -> 1200 hp. Then alternate Magic Spring III (which the Mage starts with - luckily), Healing III when required, and most important Avenging Angel III to actually damage the enemies. This involved a LOT of flying around the map to get into corners where the weakest enemies would hit my ED. For mana, I was getting +4 a round early on, and was using Mana Accelerator and the ED's Mana Drain. All of this sounds good, but it was still very, very marginal. I managed it on about the sixth attempt.
So, we've demonstrated in a few days that Defender of the Crown can be defeated on Impossible with no losses as a Mage. I suspect it would be much harder with the other classes, but if you got a good stack of Paladins I'm sure it could be done.
Had a lot of fun doing this - DotC is great as there's NO GRINDING at all. Just six main fights, all of which pose different challenges.