I don't have access to the music you're listening to, but I certainly can hear the voice and the musical character. He had that in spades and, hooked up to his charisma, it carries.
I'm not sure why you guys are dismissing his "commercial" songs. For me there are two types of commercially successful Elvis tunes: the ones I like and the ones I don't like. Among the latter are the songs with lots of overblown orchestration designed to highlight his vocal powers.
The ones I like are sparse and raw. "Heartbreak Hotel" needs only hearing that first vocal entry to understand that the entire song is wrapped up in his delivery. We've now started doing "Baby What Do You Want Me to Do," which is a great dance shuffle groove when played at his speed (as opposed to Jimmy Reed's version). I'm not sure how this was produced, because on stage was no piano and no drum kit. The guy with sticks was playing on a guitar case. Pretty hard not to be pulled in, even though he seems a little "off his dial," as Lily calls it.
https://www.youtube.com/watch?v=fDjY2VcLq7o