I haven't seen the SPTS Events or how it's different from the couple of
alternate Events web parts available (see sharepointcode.com and the MS
resource kit), but you could always bring up Team Services on a separate
box and then point a web part to something hosted on it.
Also, if you want the default view of the <server>/public/applications
calendar to be monthly, you just need to format your URL to display it
that way. I think all you need to do is add
?cmd=contents&view=monthly
to the URL and it'll show correctly.
Example:
http://srv/wksp/public/Applications/TeamEvents/?cmd=contents
&view=monthly
Create a new web part that has "HTML" as the type and gets it's content
from that URL. I forget where you have to set the permissions on it to
let lots of people, but I believe it would be in the Exchange Explorer
on the SPS server.