Thanks for the code review.  With one exception--:prefix-builtins is an option not an argument--I've incorporated your feedback.
As far as papers, I've read the information on that link several times and it appears the simplest thing to do is for me to put these changes in the public domain.  If that works, let me know and I'll remove the license and put in a disclaimer to that effect.  If not, it'll need to live in contrib as the bureaucracy seems excessive.
Thx.
--Brad
    On Friday, April 13, 2018, 1:31:53 PM PDT, Nicolas Goaziou <mail@nicolasgoaziou.fr> wrote:  
 
 Hello,

Brad Knotwell <bknotwell@yahoo.com> writes:

> Given the code review from earlier, I've added a second file with the
> requested changes.

Thank you. Some minor comments follow.

> (defconst org-babel-header-args:m4
>  '((:cmd-line . :any)
>    (:quote . :any)
>    (:unquote . :any)
>    (:list-start . :any)
>    (:list-end . :any)
>    (:prefix-builtins))

Missing allowed type for last header. Maybe :any ?

> (defun org-babel--m4-prefix (params)
>  "Prefix m4_ if :prefix-builtins is set"
>  (if (assq :prefix-builtins params) "m4_" ""))
>
> (defun org-babel--m4-changequote (params)
>  "Declare quoting behavior if start-quote and end-quote are set.  Otherwise, return an empty string."

The line is too long. The second sentence should go onto another line.

>  (let ((prefix (org-babel--m4-prefix params))
>     (start-quote (cdr (assq :quote params)))
>     (end-quote (cdr (assq :unquote params))))
>    (if (and start-quote end-quote) (format "%schangequote(%s,%s)%sdnl\n" prefix start-quote end-quote prefix) "")))

See above.

> (defun org-babel--variable-assignment:m4_generic (params varname values)
>  "Build the simple macro definitions prepended to the script body."
>  (let ((prefix (org-babel--m4-prefix params)))
>     (format "%sdefine(%s,%s)%sdnl\n" prefix varname values prefix)))

The (format ...) is not correctly indented.

> (defun org-babel--variable-assignment:m4_list (params varname values)
>  "Build the complex macro definitions prepended to the script body."
>  (let ((prefix (org-babel--m4-prefix params))
>     (list-start (or (cdr (assq :list-start params)) "["))
>     (list-end (or (cdr (assq :list-end params)) "]")))
>    (format "%sdefine(%s,%s%s%s)%sdnl\n" prefix varname list-start
>         (mapconcat
>         (lambda (value)
>           ;; value could be a numeric table entry as well as a string
>           (if (= (length value) 1) (format "%s" (car value))
>         (concat list-start (mapconcat (lambda (x) (format "%s" x)) value ",")
>             list-end))) values ",") list-end prefix)))

The line is too long. `values' should be below (lambda ...), so does
",". `list-end' and `prefix' should be below "%sdefine..."

> (defun org-babel--variable-assignments:m4 (params varnames values)
>  "Internal helper that converts parameters to m4 definitions."
>  (pcase values
>    (`(,_ . ,_) (org-babel--variable-assignment:m4_list params varnames values))
>    (_ (org-babel--variable-assignment:m4_generic params varnames values))))
>
> (defun org-babel-variable-assignments:m4 (params)
>  "Interface function that converts parameters to m4 definitions."
>  (concat (org-babel--m4-changequote params)
>       (apply #'concat (mapcar (lambda (pair) (org-babel--variable-assignments:m4
>                           params (car pair) (cdr pair)))
>                   (org-babel--get-vars params)))))

(mapcar ...) should be below #'concat.

> ;; Required to make tangling work
> ;; The final "\n" is needed as GNU m4 errors out if a file doesn't end in a newline.
> (defun org-babel-expand-body:m4 (body params)
>  "Expand BODY according to PARAMS, return the expanded body."
>  (concat (org-babel-variable-assignments:m4 params) body "\n"))
>
> (defun org-babel-execute:m4 (body params)
>  "Execute a block of m4 code with Org Babel.
> BODY is the source inside a m4 source block and PARAMS is an
> association list over the source block configurations.  This
> function is called by `org-babel-execute-src-block'."
>  (message "executing m4 source code block")
>  (let* ((result-params (cdr (assq :result-params params)))
>          (cmd-line (cdr (assq :cmd-line params)))
>     (prefix-builtins (assq :prefix-builtins params))
>     (code-file (let ((file (org-babel-temp-file "m4-")))
>                      (with-temp-file file
>             (insert (org-babel-expand-body:m4 body params) file)) file))

Last `file' should be below (let ((file ...))).

>     (stdin (let ((stdin (cdr (assq :stdin params))))
>           (when stdin
>             (let ((tmp (org-babel-temp-file "m4-stdin-"))
>               (res (org-babel-ref-resolve stdin)))
>               (with-temp-file tmp
>             (insert res))
>               tmp))))
>          (cmd (mapconcat #'identity
>             (remq nil
>                   (list org-babel-m4-command
>                     cmd-line (if prefix-builtins "-P") "<" code-file))

(and prefix-builtins "-P")

"<" and `code-file' should go below `#'identity'.

I cannot remember: do you plan to have it integrated into Org proper? If
so, have you started the process of signing FSF papers?

Regards,

-- 
Nicolas Goaziou