What a coincidence.  I started working on my website again yesterday and came up with a "solution" based analyzing the DNN 5.6 source code.

It involves minor changes to Default.aspx but....

Add this to Default.aspx:

<%@ Register Assembly="AjaxControlToolkit" Namespace="AjaxControlToolkit" TagPrefix="ajax" %>
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<ajax:ToolkitScriptManager ID="ScriptManager" runat="server" />

It's important to give the ToolkitScriptManager an ID of "ScriptManager"

This will add a script manager to every page rendered in your portal.  That's not a problem because DNN 5.6 was already doing that.  It adds a script manager in the page's init stage and then ATTEMPTS but fails to remove it after the render stage (not sure if that's by design or a coding error)

Also, for me, all of my modules subclass a common routine so I can get away with adding this code to my routine's init stage:

    

bool ror = this.ModuleConfiguration.ModuleControl.SupportsPartialRendering;

AjaxControlToolkit.ToolkitScriptManager tsm = (AjaxControlToolkit.ToolkitScriptManager)Page.FindControl("ScriptManager");

tsm.EnablePartialRendering = ror;