Remove anti-glare Coating from Viewsonic A90f+

ok guys. This is probably going to sound weird at first but please bare with me. I have had this monitor (as mentioned, a Viewsonic A90f+ CRT 19 inch) for many years. Honestly, I love this thing. A few years back, thanks to a very spaced out roommate, my monitor ended up rolling off a chair and onto a cinder block. Fortunately the monitor works, but there are a few gouges in the screen....in the most inconvenient of places. Now...first question is going to be...how thick IS the anti-glare coating on a CRT. The gouges seem to be very shallow, like I can barely snag it with my fingernail. Beneath the scratches seem a brighter, more clear image but Its only a few lines....needless to say its annoying. I really would love to get the scratches out and restore this monitor to its original beauty. So, what I need to know is a.) How likely is it that removing the anti-glare coating would take care of the scratches...and b.) how does one go about removing the coating in a manner that is safe for the glass underneath. Ive looked at alot of places but there are so many "working" solutions I dare not just randomly try one because this is all I have for a monitor. Any and all information would be Very greatly appreciated. And only solutions that are 100% safe and effective would be nice...Id really hate to ruin this thing! Thanks in advance!