I've played DE 7 times with my league lizzie team and only lost the first one, winning the other six, so I understand the problem.
As said above, blitz the skinks. Don't do much tying up of the sauri, that often goes badly. Dodge away and make it tough for the cage to move, also as stated above. Keep a blitzer deep in case a skink makes a run for it, they're tough to catch.