Someone above wrote that putting graffiti on the bag stops people from taking the wrong one, that's a great idea. I usually put some ribbon and/or coloured tape on my bags. Makes them easier to see, and less likely for someone else to pick them up by mistake.
As for the crowds, why fight them? Give it a few more minutes and then there's plenty of room and time to get your bags easily.
Trying to be first, or earliest, is like driving at 85 on the motorway, risking a ticket, instead of going 75. Over a half hour trip you save a whopping 3 and 1/2 minutes. If you really need to get there that fast, leave earlier.