For non-specialist readers:
SFT = symplectic field theory
BEHWZ = Bourgeois-Eliashberg-Hofer-Wysocki-Zehnder, the authors of the paper which establishes the basic compactness theorem for pseudo-holomorphic curves in symplectic manifolds with convex or concave ends.
There is an attractive alternative approach to SFT compactness due to Cieliebak and Mohnke:
Compactness for punctured holomorphic curves. J. Symplectic Geom. 3 (2005), no. 4, 589-654.
Their method is founded not on Deligne-Mumford-type degenerations of the source curves, but rather on the degenerations of their images in a symplectic manifold with a lengthening cylindrical neck. These degenerations are controlled by the Morse theory of the function on the source curve given by the holomorphic map followed projected to the cylindrical coordinate.