In SharePoint Online within the Administration Center, I can go to Search Center Settings and set a Search Center URL. I can do the same thing in the search service application for an on-premise instance of SharePoint 2013. I want all of my site collections by default to use this search center and this is the place to configure it.
This works great if I want Results.aspx to be the default page in my search center, but I do not. I have a custom page that I have added that I want to be the default page, but I don't see where I can make the setting to have all site collections use this page without visiting the configuration on each site collection.
I suppose I could rename Results.aspx to something else and rename my custom page to Results.aspx, but it seems like there should be a better way.
Is there a way to change the default page from Results.aspx to something else and only make this setting in one place (the search center)?
See also Manage the Search Center in SharePoint Online.
EDIT: FWIW, I looked at the SPWeb.AllProperties on a search center in my on premise SP2013 and didn't see any web property that indicated the default page was Results.aspx. There is a "__DefaultPageLayout" set to "_catalogs/masterpage/SearchResults.aspx", but I'm pretty sure that is not the answer. It could be that there is a web property for this whose default value is Results.aspx and can be added to be changed from the default. For that I might have to use a bit of reflection but it might be a dead end.