I seem to have found a glitch that happened to make progress impossible.
During a newgame+ after getting the gate key back, I went to beat Lavos from the gate at the milennial fair and unlock the last ending I didn't have in the ending gallery yet.
After thrashing Lavos, sitting through the credits, and saving the completion data, I loaded that file and went to Melchior to reforge the masamune and continue on with the plot and found that I didn't have the dreamstone. I went back to prehistory to find Ayla was not in her hut and the villagers were treating me as if I had not encountered her yet.
I don't know for sure if I didn't actually get the dreamstone, or had it and somehow lost it, as I didn't check my key items in that time.
I doubt this will be of any assistance to making a faster run, but anything altering key items might just lead in that direction.