Alrighty Lou, my first time through, I chose Offense over Magic and had basically the same experience as you (though I don't remember coming close to dying).
Your second time through was my third time through, although until now (I'm on my fifth) I'd never even tried the Ultima Weapon or the Timed Trials. Hell, I didn't even fight through with just Sora.
My second time through was Offense over Defense and I put it on expert. I can't clearly recall what went on. I think I accidentally saved over it with another playthrough.
My fourth time through, I got everything except the trials and the Ultima Weapon. Actually, I still haven't gotten the Dream Shield 'cause I haven't gotten all of the "magic Arts." The ones I've collected are Fire, Ice, Cure, Aero, and Stop. I found the Mushrooms for Gravity but don't remember where. I screwed up when I fought them, so . . .
Actually, my fifth time through didn't last long, I was trying to find some things out that you can only learn at the beginning. I hadn't even gotten to that point I was trying for when I switched to another game. I did something totally awesome and tried to save, but mid-save, somehow, my memory card slid out of place and the data became "corrupted." I couldn't save over it and had no other slots available. So, I had to sacrifice my new game for this old one. Heh.