Definitely worth trying, thanks.  I came up with:

(defun python-shell-multiline--apply-font-lock (limit)
  (let ((end (cdr-safe comint-last-prompt)))
    (if (and end (> limit end))
	(let ((font-lock-keywords python-font-lock-keywords)
	      (font-lock-syntactic-face-function
	       #'python-font-lock-syntactic-face-function)
	      (start (max end (point))))
	  (font-lock-flush start limit)
	  (font-lock-ensure start limit)))))

(set (make-local-variable 'font-lock-keywords)
       '(python-shell-multiline--apply-font-lock)))

I can verify that font-lock-ensure is being called on an appropriate region (lots of times).  With either font-lock-flush or font-lock-ensure, no actual fontification occurs.  With both of these together (as above), this error is signaled:

Error during redisplay: (jit-lock-function 179) signaled (void-function python-font-lock-keywords-level-1)

Note that python-font-lock-keywords is a *list* beginning with this symbol:

Python-font-lock-keywords is a variable defined in ‘python.el’.
Its value is
(python-font-lock-keywords-level-1 python-font-lock-keywords-level-1 python-font-lock-keywords-level-2 python-font-lock-keywords-maximum-decoration)

Not sure why jit-lock-function would be evaluating it like an sexp.

> On Apr 11, 2021, at 12:31 PM, Stefan Monnier <monnier@iro.umontreal.ca> wrote:
> 
>> But then, why bother round-tripping text out to a special-use buffer anyway,
>> vs. just letting font-lock operate in-situ in the shell buffer itself using
>> python-mode’s fairly simple font-lock-defaults. The only thing needed to
>> make this work is asking font-lock to ignore all the text with ‘field of
>> ‘output?  
> 
> Maybe you can try something like the following?
> 
>    (defvar python--font-lock-keywords ...)
>    (defvar python-font-lock-keywords
>      '(python--apply-font-lock))
>    (defun python--apply-font-lock (limit)
>      (while (< (point) limit)
>        (let ((next-boundary (find-next-boundary limit)))
>          (if (we-should-skip-this-block)
>              (goto-char next-boundary)
>            (let ((font-lock-keywords python--font-lock-keywords))
>              (font-lock-ensure (point) limit))))))
> 
> 
> -- Stefan
>