I cannot access the server using Exchange/IMAP externally. This is providing significant problems for me now since I have to spend a lot of time editing long e-mails before sending replies.
Well, braindead corporations like Microsoft will never state that you cannot do something on their braindead products like OWA, so just to put it as a statement here: no, you cannot do email quoting in OWA. Apparently, they hope that you'll figure out that you should buy Windows and Outlook if you want to do such advanced things as quoting :) (same question: webmail - Is it possible to choose a "quoted line prefix" when replying to an email in Microsoft Outlook Web App (OWA)? - Server Fault)
That being said, ilkka.github.com - Fix Outlook Quoting Style proposes using the ilkka.github.com - Fix Outlook Quoting Style proposes using Firefox with It’s All Text to open the text in a text editor, and then add the quoting prefix there...
Assuming that you are using Linux, here are a couple of alternative email clients which you could try:
Gnome: Evolution - This definitely works, but connecting to Exchnage through OWA.
KDE: Kontact - It appears that this works with older Exchange servers.