I wouldn't agree that Graham Parker & The Rumour were unhip.
When Howlin' Wind was released it was highly regarded by critics and the public. Heat Treatment likewise. However, punk did seem to sweep away GP somewhat which was a damn shame, although "Squeezing Out Sparks' was viewed as a great return to form.
I've got virtually everything he's done (on vinyl) and love it. A huge bonus is that nearly every LP sounds fantastic with great punch and clarity.
Would recommend forum members tracking down the above 3 albums at the very least.