Something went wrong with you quoting above, Shirley. Multikey is an excellent resource, which enables the user to type more than just polytonic Greek, if there should ever be a need to do so, but the polytonic Greek works just fine. As for accents, sure it's a later development, but still one developed in antiquity part of the purpose of which was to help non-native speakers of Greek better learn the language. So let's not be to dismissive of them. Such an acute rejection could have grave results, but let's stay roundly flexible on the whole subject.I've found out how to type polytonic Greek without a polytonic Greek keyboard, just by using a polytonic Unicode font with MSWord and the "insert character" shortcut keys.. Using "insert character" one can assign short-cuts for all the common Greek characters - I use "Alt + corresponding key", then save the shortcuts. It works better than any of the virtual keyboards I've tried, and my Beginning Greek students are now typing polytonic Greek with very few problems after just a couple of months, starting from scratch with the language.
To use it with BGreek messages, I type the Greek in a seperate Word .doc, and just copy and paste it into the BGreek message box.
There are a couple of doc and pdf files at http://www.drshirley.org/gr201/word-proc.html
which explain the process - and there are also some links for polytonic Unicode fonts.
I must confess, though, that I don't usually bother with the accents, unless it's to differentiate between liquid verb present and future, etc. - After all, the accents are a later development.
Hope this helps.
Multikey may be obtained here: http://www.oeaw.ac.at/kal/multikey/
It works fine with Win8.