Alfven-interchange modes in the Gas-dynamic trap (GDT) are observed to be stable under some unusual conditions, namely when the external stabilizing expander areas are turned off, i.e. are configured to have a low stabilizing curvature. We derive and study the equation that describes these modes in presence of the differential rotation and FLR effects. It turns out that though complete stabilization of interchange modes due to these effects is unlikely, the characteristic growth rates and radial extent of perturbations and, hence, the associated anomalous transport are reduced.