>> +    (while (if outline-search-function
>> +               (funcall outline-search-function)
>> +             (re-search-forward outline-regexp nil t))
>
> This changes the effect of the code because the new code searches for
> a different regexp.

Sorry, this was an attempt to unify code branches,
but this change remained untested.  Now fixed below.

>> +			(if outline-search-function
>> +                            (funcall outline-search-function)
>> +                          (re-search-forward
>> +			   (concat "^\\(?:" outline-regexp "\\)")
>> +			   nil 'move)))
>
> These two loops cons a new string each iteration.  (So did the
> original code, but if we are touching this, might as well fix that.)

This is optimized as well: