Eli, to get a free ticket that will get you to E”Y at precisely the time that you need and want to be there, is not realistic. You can daven, you can buy Chinese Auction tickets, you can try anything you want. Ultimately, you need to do some actual work to get the money for the ticket. Auction tickets to E”Y are expensive, and while the cost is tzedaka, there is no guarantee of winning.
Unless you have a rich relative who is willing to sponsor your trip, there are a LOT of worthy people out there who would love to go to E”Y, myself included, who cannot afford to go. realistically, nobody is just giving away free money for this, specifically at our convenience.
You definitely should comparison shop for the best price, though.
You want to go just before Pesach time – not an inexpensive time of year, I am afraid to say. Hatzlacha rabbah.