I always thought it was, Heartbreak Hotel. Regarding, You're a Heartbreaker, you may be right. If you could remember or find your source that said that or even the speculation of it, it would awesome.
From what I have read, Sam Phillips, had a bunch of songs from other writers and demos from bands laying around. Correct me if I'm wrong but, Elvis was called to record a specific song and it didn't workout but is that just another story like, Elvis recorded, That's All Right Momma, for his mother? ..lol
Another thing I always think about when Sun Recordings come to mind is, how Elvis at that time kept his ear on some very cool underground sounds like the version of, Hound Dog, he picked wasn't Big Momma's version. That sound was not commercialized until Elvis and yes only Elvis had guts to go 100% capturing what was considered to quote 1950s writers,"Black Music".
This sound was heard in New Orleans and Beal St, at least 20 years in passing at that point, 1955 but Only Elvis amazing abilility to mix Country with it and his wide range of music taste plus the image for the icing on the cake, made him the perfect candidate to be Crowned, "THE KING OF ROCK N ROLL"..I also think ELVIS PRESLEY, SCOTTY MOORE & BILL BLACK , should also be recognized has the creators of, ROCKABILLY.