Context. There is a class of binary post-AGB stars with a remarkable near-infrared excess that are surrounded by Keplerian or quasi-Keplerian disks and extended outflows composed of gas escaping from the disk. The Keplerian dynamics had been well identified in four cases, namely the Red Rectangle, AC Her, IW Car, and IRAS 08544−4431. In these objects, the mass of the outflow represents ~10% of the nebular mass, the disk being the dominant component of the nebula. Aims. We aim to study the presence of rotating disks in sources of the same class in which the outflow seems to be the dominant component. Methods. We present interferometric NOEMA maps of ¹²CO and ¹³CO J = 2–1 in 89 Her and ¹²CO J = 2–1 in AC Her, IRAS 19125+0343, and R Sct. Several properties of the nebula are obtained from the data and model fitting, including the structure, density, and temperature distributions, as well as the dynamics. We also discuss the uncertainties on the derived values. Results. The presence of an expanding component in AC Her is doubtful, but thanks to new maps and models, we estimate an upper limit to the mass of this outflow of ≲3 × 10⁻⁵ M_⊙, that is, the mass of the outflow is ≲5% of the total nebular mass. For 89 Her, we find a total nebular mass of 1.4 × 10⁻² M_⊙, of which ~50% comes from an hourglass-shaped extended outflow. In the case of IRAS 19125+0343, the nebular mass is 1.1 × 10⁻² M_⊙, where the outflow contributes ~70% of the total mass. The nebular mass of R Sct is 3.2 × 10⁻² M_⊙, of which ~75% corresponds to a very extended outflow that surrounds the disk. Conclusions. Our results for IRAS 19125+0343 and R Sct lead us to introduce a new subclass of binary post-AGB stars, for which the outflow is the dominant component of the nebula. Moreover, the outflow mass fraction found in AC Her is smaller than those found in other disk-dominated binary post-AGB stars. 89 Her would represent an intermediate case between both subclasses.