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Getting out of Midgar without using any materia is very easy. On my current run-through I am only using the Enemy Skill materia and running away from every battle I can. So in essence in Midgar I am doing exactly the same as you using Items, Attacks and Limits only.
Obviously during that fight Barret should attack all the time. Have you got any grenades? They will come in very handy in this fight. Aeris' healing wind is also a god send. Not sure if back rows/front rows work with this fight but if they do move everybody to the back. You could try using Tranquilizers to make everybody sad so they take less damage too and don't be afraid of using the 'Defend' option if need be.
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I was using Tranqs, I bought 3, forgetting that the effect wore off after resting >.<