If BLOCK weren't already the name of something in Common Lisp, this sort of syntax is very easy to add, easy enough to write in an HN comment. Let's call it OGOGMAD instead.

    (defmacro ogogmad (&body b)
      (cond
        ((endp b) '(progn))
        ((endp (rest b)) b)
        (t
         (let ((f (first b))
               (r (rest b)))
           (if (eq 'var (first f))
               `(let (,(rest f))
                  (ogogmad ,@r))
               `(progn
                  ,f
                  (ogogmad ,@r))))))

Exactly as you specify, this only lets you put VAR syntax immediately inside of OGOGMAD forms. (Untested, typed on mobile.)