There seems to be a wide-spread misunderstanding that the first round consists only of the first two games on Lower and Upper Egypt. It consists of four games, two simultaneously on Lower/Upper and then two simultaneously on Valley of the Kings/Nubia.
Regarding ties, I'd propose to add the squares of the players' points and compare the sums. That would weight victories more strongly; e.g. 1, 2, 2 and 3 points would lead to a score of 18 whereas 2, 2, 2 and 2 points would lead to a score of 16.
In case the sums of the squares are also the same, you could continue with the cubes etc. But if both players have exactly the same set of points, nothing based on the points alone can break the tie -- in that case other criteria like the No Cards/Escalating idea above or a tie-breaking game would be required. You could also count the number of times player A has survived longer than player B, but that works only for two-way ties, and with four games it's likely to again lead to a 2:2 tie.