I re-submitted this for 8, 8.1, and 8.2 that includes the above fix.

A small note. I tried this on a Repeater that used a Data Source, and it tried to render the webpart before the data source kicked in.

To adjust, replace the SetupControl() method with the below. This renders the control's content at the last stage (the unload) and worked.

protected void SetupControl()
{
if (this.StopProcessing || IsDesign)
{
// Do not process
}
else
{


List<Control> allControls = new List<Control>();
GetControlList<Control>(Page.Controls, allControls);
Control specifiedWebpart = null;
foreach (var childControl in allControls )
{
if (childControl.ID == WebpartID) specifiedWebpart = childControl;
}
if (specifiedWebpart == null) throw new Exception("Webpart ID Not found");

// Convert to CMSAbstractWebPart and call the ReloadData to ensure it's ready to be rendered
theControl = (CMSAbstractWebPart)specifiedWebpart;
// special case for smart search results.
if (theControl.FindControl("srchResults") != null)
{
// Search results, handle differently
var srchItem = theControl.FindControl("srchResults");
// May or may not work.
ASP.cmsmodules_smartsearch_controls_searchresults_ascx srchResults = ((ASP.cmsmodules_smartsearch_controls_searchresults_ascx)srchItem);
srchResults.OnSearchCompleted += CMSWebParts_Custom_WebpartToApiConverter_OnSearchCompleted;
}
else
{
// Attach to the Unload as it's the final step of the webpart so all data binding and stuff is complete.
theControl.Unload += theControl_Unloaded;
}

}
}

void theControl_Unloaded(object sender, EventArgs e)
{
CMSAbstractWebPart theControl = (CMSAbstractWebPart)sender;
// Build the HTML String to render the control.
StringBuilder stringBuilder = new StringBuilder();
using (StringWriter textWriter = new StringWriter(stringBuilder))
{
using (HtmlTextWriter writer = new HtmlTextWriter(textWriter))
{
writer.Write(ContentBefore);
theControl.RenderControl(writer);
writer.Write(ContentAfter);
}
}
renderOutput(stringBuilder.ToString());
}