I think the problem with a band is they will atypically say sometihng like "something similar to...but different".
So in that vain, I offer the idea that they have seen the artwork of Richard Cheese, which they like the comical approach to cover work, and they like the covers of Eli Paperboy Reed's album because they like the modern yet classic soul feel of them and they like the idea of it looking a bit like the blue note covers as well.
This does pose a slight problem as most cover art in this genre would involve pictures of the band. However singer Dan(I'm giving them names) has seen your illustrative work and would love to see if you had it in you to do a very cool illustration of the band outisde a diner on route 66 with a big sign outside the diner with the bands name on it.
This has been my experience when you are dealing with a band, general opinion and then maybe a belter of an idea.