I'm not very familiar with Egyptian technologies, but I can't see Catapults having more range than Juggernaughts (the ballista ships). Isorta remember their special technology encreases their range (not so with Greeks) so it may be equal in range.
I would have upgraded my Petsuchos so they had longer range. Then I would have loaded a few Roc's, with them. I'd have atleast 8 Petsuchos in the two Rocs, as well as two priests. I'd have two more Roc's with various regular units; probably not Migdol, they're just there to distract him and you need population room. I'd drop these units off on the other side of the river, where he has the least amount of buildings (lighthouse might help determine that). I would then have some other Petsuchos on my side of the river. I'd then have a ton of villagers build at least 6 docks. In fact, I wouldn't STOP building docks at all. The Petsuchos have what, 25 range? Since they are on both sides of the river, you should be able to reach any of his Juggernaught ships. Yes, sooner or later he'll kill your invasion army, but hopefully it'd give you enough time to build the docks.
As soon as you have a dock up, auto-que hammer-ships. They spawn fairly quickly and are the counter to juggernaughts. He was pretty stupid to go ALL juggernaughts without any archer ships. After I had three docks up, doing this, I would upgrade my hammer ships with the fourth dock. By this time your invasion force would probably be dead, but hopefully you'd have take control of the river nile.
It would be absolutely imperative to patrol the beach with fast units; I'd use Chariot Archers because they can pick off specific units. You cannot let Ouranos transport a few Atlantean villagers (heroes, most likely) over with an army for cover. The last thing you need is a sky-passage linking the two sides of the river.
It sounds like a fun game though, it's a shame that the River Nile isn't included in the random map selection I use when doing quick setup 1v1s.