The reason you can't install Beta 3 is that the one that comes installed on the phone is a system application and can't be removed or overwritten without being rooted. Here is how I got it working on mine:
1. Root the phone using Gingerbreak
2. Install Titanium Backup (I'm using premium, but I believe free should work too)
3. In Titanium, click on the backup/restore button at the top
4. Find Swype in the list and long press on it to bring up the menu
5. Choose "Convert to user app"
Now you should be able to uninstall the 2.x version and install Beta 3.