I will agree that you could end up missing Remember if you had really large crowds. I would gauge the crowd volume during the day to see if you even want to attempt this. It looks like most people wouldn't take the risk, and I can understand that, but for us, it was so worth it because we are total DEP freaks. Catching Believe was just an extra bonus.
That is exactly the key. You just need to gauge the crowds before you attempt it.
We've done it lots of times too, exactly as DM describes. You have to move fast and be good at navigating the crowds, but it is pretty easy to do, even with a stroller (and much, much easier without one!).
Sometimes, when it is especially crowded, we will run into a big traffic jam turning the corner at Engine Ears to get to the exit, and we will miss the first few minutes of the fireworks. But if the crowds are light or moderate, this isn't a problem.
Also remember that it is very easy to get a last minute fireworks spot on Main Street, even when it is very crowded. A lot of people sit down while they wait and then stand up in the last 5 or 10 minutes before the show starts, which frees up a lot of room. In two years of watching the fireworks about once a week or so, I have never, ever had a problem walking up and getting a good spot on MS at the last minute.
Also, you can stand across from Sunshine Plaza to watch the parade and then start heading over to DL about halfway through. It will get you to Main Street for the fireworks with time to spare. You'd have to miss part of the parade, but at least you'd get to see some of it.
Good luck with whatever you choose!