You actually COULD pull this off, but it would require you diving more into the Advanced Layout (something it looks like you're perfectly comfortable doing).
Your top two menus are "Login" and "Calendar". So where you have the following code, you'd have to tweak it like this (not exactly like this, but you should get the point):
Where you have this code:
<!--System:Menus:Left-->
<!--System:Menus:Right-->
You could do this
<!--System:Login-->
<div class="menus">
<h1>Calendar</h1>
<!--System:Calendar-->
<a href="adminevent.php">Add/Edit Event</a><br />
<a href="availability.php">Raid Availability</a>
</div>
<div class="base"></div>
<!--System:Menus:All:Calendar;Login;Menu-->
Keep in mind the <!--System:Calendar--> function will display the Calendar without the surrounding menu HTML (which is why we had to include it in the code for the manual display). The mention of "Calendar;Login;Menu" (note the semicolon) is a semicolon-delimited list of the menus to NOT show in that part (because we manually put them there)
All that said, admins can pretty quickly add events using the Big Calendar's Plus button, if you were unaware.