After poking around in Chrome's debugger I managed to find that ve.debounce seems to be what's changing the focus back to the edit layer.

There's a new suggestion at https://www.mediawiki.org/w/index.php?title=Topic:Sikx3284w9gfhw6t&topic_showPostId=so4tyj3gdlz0be8q#flow-post-so4tyj3gdlz0be8q

A hacky patch:

--- extensions/VisualEditor/modules/ve-mw/ui/dialogs/ve.ui.MWSaveDialog.js.old	2015-09-02 09:51:37.435374937 +0900
+++ extensions/VisualEditor/modules/ve-mw/ui/dialogs/ve.ui.MWSaveDialog.js	2015-09-02 09:46:50.733371937 +0900
@@ -480,6 +480,7 @@
 					)
 				);
 			} );
+                        this.editSummaryInput.focus();
 		}, this );
 };

All it does is add a focus to the end of the getSetupProcess function call identical to the call in getReadyProcess, which seems to fix it with both recent chrome and firefox on windows and linux. It doesn't seem to be the correct solution, but it makes it work for now without any obvious problems.