I've found the solution! This tutorial on user control events helped me substantially: http://asp.net-tutorials.com/user-controls/events/
Basically, all I did was add in a layer between the Placeholder and the View/Edit controls that handles the events and loading of each.
It basically just looks like this:
<%@ Register TagPrefix="uc" TagName="ViewMyControl" Src="stuff/ViewMy.ascx" %>
<%@ Register TagPrefix="uc" TagName="EditMyControl" Src="stuff/EditMy.ascx" %>
<asp:ScriptManagerProxy //stuff />
<asp:UpdatePanel //updatepanel stuff >
<ContentTemplate>
<uc:ViewMyControl runat="server" ID="ViewMyUserControl" OnEditItemClicked="ViewMyUserControl_EditItemClicked" Visible="true" />
<uc:EditMyControl runat="server" ID="EditMyUserControl" OnSaveEditClicked="EditMyUserControl_SaveEditClicked" Visible="false" />
</ContentTemplate>
<Triggers> </Triggers>
</asp:UpdatePanel>
Then just adding in the appropriate event firing/handling methods as described in the tutorial.
Just to reiterate: the Placeholder control in the Master Page now loads this "Manage" ascx control when you click on the corresponding Menu item instead of going straight to the View control or the Edit control, and the Manage control now handles the loading/unloading of the View and Edit controls and their respective events.