Another idea suggested by Roman, happily involving a one-line change.  Here's 
the new Note in Specialise:

Note [Auto-specialisation and RULES]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider:
   g :: Num a => a -> a
   g = ...

   f :: (Int -> Int) -> Int
   f w = ...
   {-# RULE f g = 0 #-}

Suppose that auto-specialisation makes a specialised version of
g::Int->Int That version won't appear in the LHS of the RULE for f.
So if the specialisation rule fires too early, the rule for f may
never fire.

It might be possible to add new rules, to "complete" the rewrite system.
Thus when adding
	RULE forall d. g Int d = g_spec
also add
	RULE f g_spec = 0

But that's a bit complicated.  For now we ask the programmer's help,
by *copying the INLINE activation pragma* to the auto-specialised rule.
So if g says {-# NOINLINE[2] g #-}, then the auto-spec rule will also
not be active until phase 2.