First thing I noticed is that you are playing the vanilla game (not RnF or GS xpacs). The warfare is a bit simpler there, as you do not need to worry about loyalty.
Second, strategically, you are pushing with a too small force. Three bombards are fine, but you cant leave them exposed to much city/encampment fire and vulnerable to cavalry. One (!) melee and one (lagging behind) cannon don't do enough for protection. Also, for efficient siege you need to eliminate city healing, which needs three units with zone of control, in some cases two, but these cities are in open. Also, for taking a city you need a melee/cavalry unit. Ranged and siege cannot walk into cities. Your enemy is of comparable strength - one does not simply walk into Egypt, one needs eight companions.
Tactically, movement is key. You must expect in rough terrain one tile-per-turn movement, that exposes your forces for longer time. Bring more or pick easier target first. Shedet could be easier, not sure how well it can be bombarded, if it's two or three tiles - in that case the walls should crumble within two turns. You can't slip past the encampment to Ra-Kedet or Abydos, that leaves you vulnerable for too long. Generally, you want melee or cav to go first to siege/stop city healing and pick off units, then pull siege units to crush walls. The front units should be able to heal by pillaging by then. Additionally, pillaging districts lowers city defence, like 2 per district.
As for planning an invasion, the route Thebes-Abydos-RaKedet looks good. Shedet-RaKedet would be my pick, as its only one-two steps from your border as well, and has nice road and undefended terrain. If you wanted an easier alternative target with more to pillage, Shedet-Edfu looks promising, especially if that encampment belongs to Shedet.