What if the EotG gave a 6+ save after the save on everything in a bubble? It would make it a little more viable in matched play. Not that it's bad but it would also help with Saurus guard. Maybe give it a prayer that makes it got to a 5+?
Though it'd make the engine better it'd still make it a mess of a unit with no consistent purpose. It's random effects first need to all have the same requirements and all fullfill the same niche (or at least the requirements and niches should be similar enough...). As long as it's so over the place in what it can do it's unreliable and you can't build a proper strategy around it. The designers need to make up their mind what they want the EoTG to actually do in an army. As for the effect itself, yea that bubble would be briljant and help a lot with some of our supectiblity to mortal wounds, though I wouldn't put it on just an EoTG I'd just make it a prayer for our priests alongside several other options much like the prayers the SCE get for example. If wanted the EoTG could then have a more powerfull version of the prayers compared to our unmounted skink priests.
A while ago we talked about several possibilities of how to change stuff for the EotG but... still too random for me. Your idea would add one ability that is reliable, which would surely help, but I agree with @Canas that the main problem probably isn't solved with it. Here is the old thread if you are interested in reading a bit more about our thoughts concerning the EotG: http://lustria-online.com/threads/eotg-effect-replacing-summon.20725/