The Costas Arrays Problem seems to not benefit from constraint propagation very much. These slides by Helmut Simonis have a good demonstration of limits of propagation when solving it, some improvements over a naive model via adding implied constraints and trying a better search strategy. Don’t be scared of the 877 slides, the slide deck contains some very nice animations of the propagation and search behaviour of 3 variants of the model and search strategies.
This website maintains a list of known results.
A paper by Drakakis et. al. [drakakis2011results] presents a study where the authors spend 366 machine years on the order 29 problem and do not find anything new.