I'm sorry, I still can't read the slogan in any of the versions. Also, I like the JD logo imitating a bun and ice cream, but it is not obvious enough--several people had no idea that it was a JD and/or bun and ice cream.
If you google Burgerparlour in UK, that is more what we are thinking of.
Also, we would like to get away from generic 'restaurant' term and have something more descriptive/creative, ie 'grille and parlour', 'sandwich and ice cream shoppe', ect.....