I think you can side-step the fidgetiness of the layer control mouseover if you instantiate the layerControl with the GEM_base layer included. See http://leafletjs.com/reference.html#control-layers-l.control.layers.

This matches what we've done in the exposure export tool: https://github.com/gem/oq-platform/blob/master/oq-ui-client2/src/exposure/exposure_export.js#L85