I've always loved this piece of music, too, and although I'm not an expert on ReMixing (I've never submitted one of my own before, although I've always wanted to, I can't afford the equipment), I can certainly give you an opinion. I absolutely love MMIII and its music, so I hope that might be of some use to you.
I'll be honest, the first time I listened, I felt that the beginning was a bit drawn out. As the instruments were first layered on, I tried to hear a melody, and sat there thinking to myself that either
a)I was an embarrassment to Mega Man fans everywhere for not recognizing the theme,
or
b)It was so heavily modified that the theme was not discernible.
Finally, after about a minute and a half of listening, the theme came in, but I felt that the layered instruments blocked it out a bit too much. However, when the noise of all the instruments died out (I loved how you faded to nothingness), and the theme itself kicked in on its own, a bit more calmly on the stringed instruments (with some nice harmony built upon them immediately after), I truly began to appreciate the contrast you had put in place. The huge, layered crescendo running through the first couple of minutes of the ReMix made a lot of sense at that point, and I commend you for pulling it all off so well. There are many more nice things running throughout the piece, and I particularly like the great number of slightly different incarnations of the main theme, throughout, with the differences in speed and dynamics making each one unique in its own way. The beat is strong throughout, and the dynamic contrast is something that, although I didn't fully appreciate it at first, serves as a huge highlight in this nice piece you've created.
The next time I listened, I actually liked the extensive nature of the introductory sequence, now that I knew that the theme actually did come in, and was completely recognizable. It made more sense going with the dynamic contrast I discovered later in the first listening, and I would not suggest really changing anything at all. I didn't like it so much at first, but your creation quickly grew on me, and I feel it has a good chance of getting through the judging panel if you submit it.
Anyway, I hope this helps, and good luck on getting your ReMix accepted