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I believe the framework of chess can be addressed now so that we never turn
chess into a solved game.  I personally believe there is part of the answer
in a game like Seirawan Chess, or a pocket version with reserves, but I
don't think they alone have the answer.  It also doesn't address the
framework issue either that gets chess stuck, and all the classic abstract
strategy game (stuck here means set on a path to being 'solved', without
a way to adjust before it does).  

My take on Godel's Incompleteness Theorm is that you don't solve the
systemic issues with a certain set of rules by creating more rules of the
same type.  If it is show, for example with chess, that a set
configuration of chess pieces on the board eventually produces something
that is solved, then changing the configuration of the pieces on the board
alone doesn't resolve it either (one time, fixed).  You can change the
their starting position (aka Chess960/Pick your Army/MetaChess or the V
and X versions of IAGO Chess), the layout of the board at start (and also
changing it during play, aka Beyond Chess), or when the pieces enter the
game (IAGO/Seirawan/Pocket Knight/Pocket Mutant), and help to push things
out further.  If you build into the framework by which you can do all of
the above, you buy more time.  What regular chess has now is not a way to
make chess get 'unstuck', allowing it to adjust over time.  I suggest
all of the above be considered and integrated, and the players settled on
what works best.   Eventually even this mix of everything leads to a
'stuck' position as the playing community may figure out what is
optimal.  By then, some other people will need to come up with another
layer of rules to insure things are unstuck.  

I can't say this for certain, but I do know unsticking chess by doing all
of the above should likely buy chess another 1000 years, using all of the
above methods described.  The key to having it get unstuck is to have it
done in a way that it is evolutionary, so the playing community can
migrate over time and get used to the changes.  Also added to the mix are
'mutators' which are meta-changes to how the game works that get added
during play.  PlunderChess, for example, is built on a mutator that is
active from the start, pieces fusing together.  Even these added can have
an impact, and force people to think more creatively, relying on
principles.  These changes act as weather, and another key element to
getting chess unstuck (and other abstract strategy games for that matter).
 All these elements help to battle to keep a game from getting stuck,
without the use of random element, or hidden information, which is the
standard method used to unstick a game.  Like, the case of backgammon,
luck prevents it from getting stuck for a long time.  Stratego uses hidden
information, and the bluff element causes players to play other players. 
In this you need to know your opponent more than the environment.  Because
of this, a game like poker can be played even 1000 years from now, because
you play the players, and luck also offsets (hidden information+luck). 
Magic: The Gathering, and also Cosmic Encounter also relate to this, which
has in its makeup things that continue to change the rules.  I believe such
mutators can be applied to a game like chess, but not in such a chaotic
manner.  In other words, you can have a game that is a pure abstract
strategy game, but where the rules do change during the course of a game,
if the players control when the rules come into effect and the potential
rules are fully known by all players in the game. 

Please feel free to comment here.