I'm a native English speaker and "rural" is a genuinely weird word to pronounce. My pronunciation is halfway between "earl" with a leading "r" and just incoherently growling "rrrl".
I was thinking the same thing - I realized that when I say this word, it is always slurred. Your pronunciation is much like mine, and I'm not even sure it would sound correctly if it were different as it would put too much emphasis on the middle "r".
However, I'm sure there is a name for that "there but not there" letter.
