I've heard back from Pipeten & they have confirmed that the .NET version my server is using (dwin41) is running .NET 4.6.1, with my own application pool running in Full Trust.
I have tried commenting out the <system.xml.serialization> section again (as per default web.config) and that doesn't seem to have made any difference (I think I added that when having problems in Medium Trust a few years ago). There again, looking at the System Log I see these entries:
2017-04-21 12:32:00,622 INFO (null) - (null) - (null) - mojoPortal.Web.Global - Application Started.
2017-04-21 12:32:01,231 INFO (null) - (null) - (null) - mojoPortal.Web.WebTaskManager - deserialized WebTaskManager task
2017-04-21 12:32:01,262 INFO (null) - (null) - (null) - mojoPortal.Web.WebTaskManager - Queued WebTaskManager on a new thread
Would the deserialized entry suggest I should revert to the extra serialization entry?
I also tried removing the comments around:
<remove value="Default.aspx" />
<add value="Default.aspx" />
However this seems to cause an error "The page cannot be displayed because an internal server error has occurred". Putting the extra comments back gets rid of the problem.
Neither bits of editing makes any difference to the Admin Cog working though...