Without hard-coding in the template (and maybe that is the way) how can I change the link for "All events" in the Events template single item view to link to a different page other than to itself as it seems to do by default?
Yes, you can set this in the template, or you can set the MasterPageId property in the widget by clicking on Edit>>Advanced>>Home > ControlDefinition > Views > EventsFrontendEdit to the Id of the page you want to set.
Note however, that both settings will replicate an already existing functionality in the Events widget designer to specify single event items to open in another page (please see attached screenshot). My point is that even though you might set the All Events link to a different page, once you click on all items you will be redirected to the desired page, but if you click on an event on that page, this single item will be opened automatically in the same page, unless you also set the
<sf:DetailsViewHyperLink TextDataField="Title" ToolTipDataField="Description" runat="server" />
in the template for ListItems.
I hope this information helps. If you need any further help accomplishing the desired functionality, please do not hesitate to contact me.