If you are not using Real Weather Connector, I think setting the overcast setting to "solid procedural" would work around the issue.
If you are using Real Weather Connector, the procedural options for overcast generally don't get used. In that case things get more involved; because the overcast clouds consist of large billboards, we fade them out close to the eyepoint in order to avoid distracting anomalies when you get too close to them. This is especially an issue in VR.
But, you can disable this effect by editing the file Resources/plugins/SilverLining/resources/silverlining.override, and looking for this line:
stratocumulus-particles-distance-fade-length = 0.5
If you set that to 0 instead of 0.5, I think it might help. We don't normally endorse modifying this file, but if you need this for real training it's worth a shot.