Maybe something like this (tested with LaTeX and HTML)

    #+TITLE: An Orged Paper
    #+AUTHOR: Rasmus
    #+DATE: A Dark Day for Science 

    #+RESULTS: html-header

    #+begin_abstract
    #+begin_center
    {{{html-only(*Abstract*)}}}
    #+end_center
    my long abstract that is longer than one line. my long abstract that is longer than one line.
    #+end_abstract
    #+toc: headlines
    * Introduction
    Please read my paper!
    * Data
    ~{0,1}~
    * Conclusion
    Something deep and profound

    {{{html-only(------------)}}}
    * styles                                                           :noexport:
    #+HTML_HEAD_EXTRA: <style type="text/css">
    #+HTML_HEAD_EXTRA: <!--
    #+HTML_HEAD_EXTRA:   .header_title {font-size: 2em; font-weight: bold;}
    #+HTML_HEAD_EXTRA:   .header_author {font-size: 1.5em; font-weight: bold;text-align:center;}
    #+HTML_HEAD_EXTRA:   .header_date {text-align:center;}
    #+HTML_HEAD_EXTRA:   .header_date .timestamp {font-size:1em; color:#000000;}
    #+HTML_HEAD_EXTRA:   .abstract {max-width: 30em; margin-left: auto; margin-right: auto;}
    #+HTML_HEAD_EXTRA: -->
    #+HTML_HEAD_EXTRA: </style>

    #+OPTIONS: toc:nil

    #+MACRO: html-only (eval (if (org-export-derived-backend-p org-export-current-backend 'html) "$1" ""))

    #+NAME: html-header
    #+BEGIN_SRC emacs-lisp :results raw :exports (if (org-export-derived-backend-p org-export-current-backend 'html) "results" "none")
      "#+begin_header
      ,#+begin_header_author
      {{{AUTHOR}}}
      ,#+end_header_author
      ,#+begin_header_date
      {{{DATE}}}
      ,#+end_header_date
      ,#+end_header
    "
    #+END_SRC