So it turns out it was the MimeBodyPart headers after all,
I had to set the Content-Type to "text/calendar;method=REQUEST" and remove the setting of the filename
This link provided me with the solution:
http://valermicle.blogspot.com/2009/02/i-was-searching-for-documentations-on.html
There still needs much work customizing the SendIcal.java class so that we're not using hardcoded values, but now outlook is recognizing the .ics attachment as an actual calendar event!