Extending the standard model to include gravity, and thereby creating a "TOE" (Theory of Everything), is not I think going to be hurt by Godel. Because for TOE to work, all it need do is make predictions over and above the standard model, which can be verified by experiment, but also be consistent with all predictions of the standard model. If it can do this, it will stand as a TOE, at least until it disagrees with prediction, if and when that would happen. In other words, a TOE need not be "provable to be consistent in all it axioms". All it needs to do is include the Standard Model's predictions, then, make a few new ones to include gravity. Like one nice prediction would be to have the value of 10^-120 plank units for the energy density of "dark energy" arising naturally and nicely from someplace. That would be a good prediction, just as an example. If a TOE (inclusive of the standard model, plus a description of gravitons which delt with infinities), could regurgitate all standard model predictions, plus just make one prediction more (like setting the energy density of dark energy without having to appeal to the anthropic principle, mind you), then we got a good TOE. "Provable?" No. But it lives to fight another day, which is the best we can ask of a theory anyway.