In case I want to grok this in 6 months.

(define (whatdoicallthis lst func)
  ;; Grab pointer to first cons.
  ;; Contents of car will be dropped.
  ;; Contents of cdr will be clobbered. 
  (let ((newlst (list #t))) 
    ;; acc is usually the result of the
    ;; "reduce so far", here it is the
    ;; last pair in newlis. cur is
    ;; current item of consideration
    ;; in the original list. 
    (lfold (lambda (acc cur)
	     ;; func should return a new
	     ;; pair, which gets tacked 
	     ;; onto the end of newlst.
	     (set-cdr! acc (func cur))
	     ;; Have lfold push the new
	     ;; pair into acc next
	     ;; time it loops.
	     (rest acc))
	   newlst ; Accumulator
	   lst) ; list we're deriving from
    (rest newlst))) ; car is trash, see above.

(define (append hd tl)
  (whatdoicallthis hd (lambda (nxt) 
			(cons nxt tl))))

(define (map func lst)
  (whatdoicallthis lst (lambda (nxt) 
			 (list (func nxt)))))

Woo!

Got it.

(define (whatdoicallthis lst func)
(let ((newlst (list list)))
(lfold (lambda (hd tl)
(set-cdr! hd (func tl))
(rest hd))
newlst
lst)
(rest newlst)))

(define (append hd tl)
(whatdoicallthis hd (lambda (nxt) (cons nxt tl))))

(define (map func lst)
(whatdoicallthis lst (lambda (nxt) (list (func nxt)))))

A step closer…

(define (append hd tl)
(let ((newlst (list list)))
(lfold (lambda (hd nxt)
(set-cdr! hd (cons nxt tl))
(rest hd))
newlst
hd)
(rest newlst)))