Is there anyway to make Azureus download speed stay stable at a high rate?

You can't Actually connect to all peers and you don't have to. Open your torrents by double clicking and check the availability make sure it is over 1. (if not you can't have the full file until you do. Also to speed up torrents change your cache to NO more than 32, I use 32MB cache and by god it speeds things up. Refer to the wiki as much as possible.