I had a similar issue after I upgraded to 4.8.2 (when using a Rad Ajax / Multi-Page / Tabstrip / Gridview set of controls) - I got the same error (he Controls collection cannot be modified because the control contains code blocks (i.e. <% ... %>). - when switching indexes in the TabStrip.
Your suggestion of checking the "Supports partial page rendering" did the trick for me - and the error went away.
I didn't think I needed that, because in my code behind I would always put in the following in the Page Load.
If DotNetNuke.Framework.AJAX.IsInstalled Then
DotNetNuke.Framework.AJAX.RegisterScriptManager()
End If
However - after I examined my code - I see I forgot it on this control (must be why it broke after the upgrade). I went back and put it in the Page Load, unchecked the "Supports Partial Page Rendering" in module definitions - and it worked. (I am presuming that the Ajax fix for 4.8.2 had something to do with this one).