As far as I know you can't replace the home page tab but you can control what is placed in the tab. Try this:
 
1.) Goto Setup->Customize-Home->Home Page Components
 
2.) Click New under Custom Components
3.) Click Next
4.) Give it a name, select HTML Area and click Next
5.) In the Formatting code section on the far right hand side click the Show HTML box
6.) In the body of Formatting code place 
1<iframe src="<full path to your page>"></iframe>
   note: you may have to adjust the frame size to get it to look right for you
 
7.) Click save
8.) Goto Setup->Customize-Home->Home Page Layouts, click New, give it a name and Save
9.) Under Select Wide Components to Show choose your new component ad click Next
10.)  Make sure your component is the only one selected in Wide(Right) Column on the next page and click save.
11.) You'll now be back on the Home Page Layouts screen. Click Page Layout Assignment and add the layout to the users whos home page you want to modify.
 
It's kind of a hack but the users will now only see their Chatter feed (if enabled) and the page you just added (your leaderboard page) if you've followed the steps correctly above. Of course the page will show the sidebar and header if you haven't disabled them on your custom page so keep that in mind.