For reasons unknown to me, our Exchange Team manager wants us to
remove the My Inbox and My Calendar from the My Site home page. I've
done this by modifying the Shared Page, but that did not
satisfy "the powers that be". I'm now being asked how to remove them
permanently so that they cannot be re-added.

I recognize that even if I remove them so that they can not be re-
added, users can still add them inbox and calendar using the content
editor web part (cewp) and the trick of using an <object> tag with
the guid as outlined at:
http://www.wssdemo.com/Pages/OutlookDemo.aspx

In looking into this dilemma, I noticed from the Onet.xml file that
the web part is implemented in the assembly
Microsoft.SharePoint.Portal and uses a type name of
Microsoft.SharePoint.Portal.WebControls.OWAPart. Since it's in that
particular assembly, is there really any safe way to prevent users
from adding those web parts back to their My Site home page without
having other serious consequences to the site?

I've also found this admin page:
http://hostname/personal/[username]/_catalogs/wp/Forms/AllItems.aspx
which allows me to "delete" these web parts, but deleting them from
this list didn't seem to have any effect whatsoever. I can still re-
add them to My Site as if I hadn't deleted them.