I don't think people are going to be willing to post cover letters they believe give them an advantage in procuring REO listings. Besides, if you want your letter to be noticed, it doesn't need to be a cliff notes version of 500 other letters they have received.
Just tell them why you would be a good REO agent. Are you familiar with property management? Are you a commercial agent/broker or a residential agent/broker? Do you understand short-sales, foreclosures, deed-in-lieu, etc.?
Most importantly, do you understand the banking process behind the REO business. That was the hardest for me when I started, was learning to think like a banker, as this will have an effect on how the deals are done, and often times how the contracts are drafted. You need to understand why it takes so long to get a response on offers and prepare your buyers for that contingency. etc., etc.
Contact REO agents in your area and ask if they need any help, would be willing to let you tag along on a deal, or let you help work up a BPO on a property. In my experience, most REO agents got their foot in the door from other REO agents. Make friends, learn from them, and soon you will know which banks to contact and what they are looking for in an agent. Do they just want you to do BPO's or do they actually want you to list and market the property? Some REO agents have no listings, they simply perform BPO's for the banks at a set price. Which agent do you want to be?
Hope I was some help.