A quick internet search showed that the gag has been done before (mostly as a meme) but only half-heartedly: putting pointy ears on Elvis; Legolas singing Love Me Tender; or throwing in some Tolkien-ish words into some of Elvis' songs.
My thought that the gag should be like Elvis: a little over the top! Singing his songs in Elvish, wearing rhinestone-studded Woodland elf clothes! And definitely not the fat Elvis! I tried rendering the lyrics he's singing into an Elvish script, but part of the fun of the joke is almost recognizing the lyrics.*
When I report back on the training, I'm going to have to say that I may not have gotten much out of it, but I thoroughly enjoyed it!
*If you're interested, we could get into a side discussion on the theory of humor. Any takers?