If they are as you describe "large" scratches, then I don't think there is a way of removing them. I have tried numerous products over the last 30-odd years which claim to do so, including cerium oxide (jewellers rouge), but have found that if I could feel the scratches with my finger-nail, removing them was impossible. I have on a few occasions replaced the front panel of glass to solve the problem.
Have you ever tried using one of the kits that are available for repairing car windscreen chips/scratches? They inject a clear resin into the blemish which you can then polish out to leave an "as new finish", (if you believe the advertising bumph ).
I've not tried it but someone with your knowledge of glass may want to.
like you guys have said jewlers rouge is next to useles for big scratches, the resin is an option but if it doesn't work then you have no chance of ever removing it without making the scratch worse. either way you will have to empty your tank so you may as well just turn it round as suggested