Launching systems that use in sequence more than one mirror to direct and focus electron cyclotron (EC) waves with a sufficient steering capability in relevant absorption regions of fusion plasmas may produce general astigmatic beams. The double curvature of a generic reflecting surface, even induced by deformation effects in quasi-optical systems that handle high power, is an additional source of general astigmatism. Describing the propagation of general astigmatic Gaussian beams is a necessary step in the optimization phase of a complex EC resonance heating (ECRH) launcher, since simple astigmatism treatment does not reproduce the main feature of these beams, whose spot and phase ellipse orientation changes with propagation even in free space. The correct orientation for both spot ellipse and phase ellipse is one of the input key parameters to perform realistic calculations with beam-tracing codes, which aim to characterize a launching system in terms of localized heating and current drive efficiency. In this work we describe the influence of double-curvature effects and deformations on beam propagation in terms of beam dimensions and directions. In particular, we present an application of the theory of general astigmatic Gaussian beam propagation in vacuum to the case of the remote steering option for the ITER ECRH upper launcher. In this option beams are found to be strongly astigmatic, with a major/minor axis ratio in relevant absorption regions ranging from 2.3 to 4.4 in the cases examined. Furthermore, the major axis of the resulting spot ellipses presents an orientation angle variation (from the last mirror to the expected absorption regions) ranging from 9.1 to 22.8 deg in the cases investigated. The final orientation is close to a vertical direction with respect to the equatorial plane of ITER.