Spin 2 just means that the gravitational field is given by a metric field and general covariance, which is the nonlinear expression of a massless spin 2 representation of the Poincare group. The latter appears when linearizing around the Minkowski metric and dropping all interactions.
See the classical paper by S. Weinberg, Phys.Rev. 138 (1965), B988-B1002
and the entry ''Why do gravitons have spin 2?"" in Chapter B8: ''Quantum gravity'' of my theoretical physics FAQ at http://arnold-neumaier.at/physfaq/physics-faq.html
It is not true that only the linearized gravitational field can be quantized.
Currently perhaps the best synopsis of canonical nonlinear quantum gravity is the following paper:
R. Brunetti, K. Fredenhagen, K. Rejzner,
Quantum gravity from the point of view of locally covariant quantum field theory, 51 pages
http://arxiv.org/abs/1306.1058 (Submitted on 5 Jun 2013)
Abstract: We construct perturbative quantum gravity in a generally covariant way. In particular our construction is background independent. It is based on the locally covariant approach to quantum field theory and the renormalized Batalin-Vilkovisky formalism. We do not touch the problem of nonrenormalizability and interpret the theory as an effective theory at large length scales.