Completing myself, here is a patch implementing the previous suggestion,
along with example output obtained with it.  You may need to
(fmakunbound 'org-e-ascii-target) to avoid an error, since this patch
removes the function.


First, the test buffer.


#+begin_src org
#+TITLE: Cross-references
#+LANGUAGE: en

* First headline.

  Here we demonstrate cross-references to items.

  1. A first item in a list.
  2. Another item
     1. With three subparts. This one.
     2. Another one.
     3. <<itm:last>> And the last subpart.
        
  We end the list at item [[itm:last]].

  Before we continue, here is a rather trivial equation, assuming base
  isn't too low[fn:1].
  
  #+name: eq:trivial
  \begin{equation}
  1 + 1 = 2
  \end{equation}

  We can verify it with the following code:

  #+name: oneplusone
  #+caption: Shortly after the beginning of arithmetic.
  #+BEGIN_SRC emacs-lisp :exports code
  (+ 1 1)
  #+END_SRC

** Sub-topic

   Here we demonstrate cross-references to tables.<<sec:tables>>

   #+name: tab:numbers
   #+caption: Test
   | one | 1 |
   | two | 2 |

   #+name: tab:letters
   #+caption: Letters
   | a | aille |
   | b | bi    |

   In table [[tab:numbers]] we can only see two numbers.  Yet, in [[tab:numbers][the very
   same table]], we can already tell the radix used isn't too low
   (remember footnote [[fn:basetwo]]?).  On the other hand, table
   [[tab:letters]] shows letters, but that's clearly uninteresting.

   #+name: eq:euler
   \begin{equation}
   e^{i\pi} + 1 = 0
   \end{equation}

   Equation [[eq:euler]], also known as Euler's equation, is remarkable
   unlike to the equation [[eq:trivial]], which is boring (except the
   elisp part, in listing [[oneplusone]]).

   #+target: end
   This is the end of section [[sec:tables]]. [[end][Invisible link to line above]]

* Footnotes

[fn:1] <<fn:basetwo>> That is strictly greater than two.
#+end_src



Then the ASCII output.



#+begin_src text
1 First headline.
=================

  Here we demonstrate cross-references to items.

  1. A first item in a list.
  2. Another item
     1. With three subparts. This one.
     2. Another one.
     3. And the last subpart.

  We end the list at item 2.3.

  Before we continue, here is a rather trivial equation, assuming base
  isn't too low[1].

  \begin{equation}
  1 + 1 = 2
  \end{equation}

  We can verify it with the following code:

  ,----
  | (+ 1 1)
  `----
  Listing 1: Shortly after the beginning of arithmetic.


1.1 Sub-topic
~~~~~~~~~~~~~

  Here we demonstrate cross-references to tables.

   one  1 
   two  2 
  Table 1: Test

   a  aille 
   b  bi    
  Table 2: Letters

  In table 1 we can only see two numbers.  Yet, in the very same table,
  we can already tell the radix used isn't too low (remember footnote
  1?).  On the other hand, table 2 shows letters, but that's clearly
  uninteresting.

  \begin{equation}
  e^{i\pi} + 1 = 0
  \end{equation}

  Equation 2, also known as Euler's equation, is remarkable unlike to
  the equation 1, which is boring (except the elisp part, in listing 1).

  This is the end of section 1.1.
#+end_src



And with LaTeX.



#+begin_src latex
\section{First headline.}
\label{sec-1}

Here we demonstrate cross-references to items.

\begin{enumerate}
\item A first item in a list.
\item Another item
\begin{enumerate}
\item With three subparts. This one.
\item Another one.
\item \label{itm:last} And the last subpart.
\end{enumerate}
\end{enumerate}

We end the list at item \ref{itm:last}.

Before we continue, here is a rather trivial equation, assuming base
isn't too low\footnote{\label{fn:basetwo} That is strictly greater than two.}.

\begin{equation}
\label{eq:trivial}
1 + 1 = 2
\end{equation}

We can verify it with the following code:

\begin{figure}[H]
\caption{\label{oneplusone}Shortly after the beginning of arithmetic.}
\begin{verbatim}
(+ 1 1)
\end{verbatim}
\end{figure}

\subsection{Sub-topic}
\label{sec-1-1}

Here we demonstrate cross-references to tables.\label{sec:tables}

\begin{table}[htb]
\caption{\label{tab:numbers}Test}
\begin{center}
\begin{tabular}{lr}
one & 1 \\
two & 2 \\
\end{tabular}
\end{center}
\end{table}

\begin{table}[htb]
\caption{\label{tab:letters}Letters}
\begin{center}
\begin{tabular}{ll}
a & aille \\
b & bi \\
\end{tabular}
\end{center}
\end{table}

In table \ref{tab:numbers} we can only see two numbers.  Yet, in \hyperref[tab:numbers]{the very
   same table}, we can already tell the radix used isn't too low
(remember footnote \ref{fn:basetwo}?).  On the other hand, table
\ref{tab:letters} shows letters, but that's clearly uninteresting.

\begin{equation}
\label{eq:euler}
e^{i\pi} + 1 = 0
\end{equation}

Equation \ref{eq:euler}, also known as Euler's equation, is remarkable
unlike to the equation \ref{eq:trivial}, which is boring (except the
elisp part, in listing \ref{oneplusone}).

This is the end of section \ref{sec:tables}. 
#+end_src


Regards,

-- 
Nicolas Goaziou