I know for sure that the shadow quality of objects depends on the lightmap of the object that’s having its shadows rendered. I believe it can be increased by changing the Lightmap Resolution of the object (I think that’s the way). If you open the object in the static mesh editor and in its details, scroll down to look for Lightmap Resolution (it’s usually set to 64), if you try increasing it in increments of 2 (8/16/32/64/128/256~) and see if the shadows sharpen up a bit. Is your light-build quality set to Production or Preview? You can choose how well the lighting is built by clicking on the arrow next to “Build” on the toolbar, then under Lighting Quality, change to Production. It takes longer to build the scene, but the lighting will be much better than Preview quality.
Also an added something is that if you have a large map, or even a normal size map, but want the light build to render a specific section of the map, you can use a Lightmass Importance Volume, which will build lighting only for the zone contained within it. It’s under “Volumes” in the “Modes” menu on the left side above content browser. I believe there are a lot of settings to getting shadows to look right that go beyond just static vs stationary though. But you’re welcome!