O.K., Nigel, I'm confident now I know what you mean (and why I didn't get it first):

On the assumption that they see what George does Fred shoots to miss and Ernest kills George (for sure). Next to shoot is Fred and they both have the same probabilities to survive as before just a bit higher for the elimination of George.

I have two problems with that solution:
(1) Ernest realising what has happened might shoot to miss as well for that increases his probability to survive (someone of the others might get nervous next time) and after some rounds they all find out that never hitting each other is the best possibility.
(2) I always thought that George's best strategy is to shoot to miss but in a way nobody of the other two realises what he does. A 60% shooter should be able to feign intention to hit when he hasn't. In that case, the above solution doesn't work for the other two are not able to spot George's intention.

You could say, however, that merely by thinking it through they should realise that George must have the intention not to hit the first for his own benefit...

Wolfgang