There has been a great deal of progress in Shape Dynamics in the last few years. Much of it due to Koslowski, Gryb and Gomes who have extended Barbour's best matching principle from a Lagrangian formulation to a canonical one. This has allowed them to develop the method of gauge symmetry trading, with which they have constructed Shape Dynamics as a theory which is dual to General Relativity in a particular gauge fixing.
By "dual" I mean the two theories are locally equivalent, everywhere giving the same equations of motion. This is similar to the ADS/CFT correspondence except at a fully classical level.
This trading of symmetries allows them to resolve two facets of the long standing "Problem of Time" which has plagued Quantum Gravity research, "many fingered time" and the "frozen formalism".
Some recent papers:-
"The shape dynamics description of gravity"
Tim Koslowski
http://arxiv.org/abs/1501.03007
"The Solution to the Problem of Time in Shape Dynamics"
Julian Barbour, Tim Koslowski, Flavio Mercati
http://arxiv.org/abs/1302.6264
"Identification of a gravitational arrow of time."
Julian Barbour, Tim Koslowski, Flavio Mercati
http://arxiv.org/abs/1409.0917
"A Shape Dynamical Approach to Holographic Renormalization"
Henrique Gomes, Sean Gryb, Tim Koslowski, Flavio Mercati, Lee Smolin
http://arxiv.org/abs/1305.6315
There was an interesting exchange between Lee Smolin and Julian Barbour at the end of Barbour's presentation at the Perimeter Institute where Smolin asks something like "rather than eliminate time haven't you found a universal time?" Barbour agreed that was a reasonable interpretation.