Well, your "problem" and your question aren't necessarily related. I know that LA, much like my market, is very competitive for the best deals. You should also know that homes that are priced well see multiple offers and often sell above list price. It sounds a bit unusual that within 1 or 2 days a bank owned property would go under contract; I find that takes a week even if they get multiple offers on the first day it's listed. Below is a post that explains the types of transactions you'll find out there; and you can click on the links for even more detailed information. But, be prepared to move quickly when a house comes on the market that you might like. Make sure you're getting the alerts about new listings that fit your criteria right when they come on the market; and then plan on seeing it right away and being ready to write an offer on the spot if it is the right house. Understand you may end up writing on a few before you get a contract ratified. If there are 5 offers on a property, you only have a 20% chance, and the way to increase your chance is to prepare a strong offer.
To answer your question... I'd say a strong "foreclosure" agent is one that understands the differences between foreclosures and other types of sales and can guide you accordingly. By reading the blog below, you will be able to ask educated questions and know that you're dealing with a pro.
By the way, the reason I have a clue about the LA market is because I have an agent out there that I exchange quite a bit of business with. He's excellent, and the people I've referred him to become his friends. If you'd like a referral, please email me with your name and contact info and just a bit about the type of home you have in mind. If it fits his business model, I will put you in touch.