Thanks for the info!***NOT LEGAL ADVICE***
I will most likely file it this week (I have some tight deadlines with my US Visa , so have to go down this route). I talked to a lawyer who listed 3500CAD for filing Mandamus. I'm about to speak to another lawyer who quoted around 1000CAD.
This is just for filing which should most likely be sufficient for me to get a decision within a month. Since your case is complicated, it might go into arbitration and court proceedings in which case it would cost much higher.
Good luck to you! I hope you will meet your deadline and all will turn out well for you.