wet dry sand paper from an auto detailing shop, get 2000, 4000, 8000, and 12000 grit. get a small block of acrylic, or other non reactive material to use as a sanding block. sand as normal, with the exception of your arm being submerged in the tank. the fine acrylic dust is completely inert.
start with 8000 sanding directly over the scratch. if it doesnt diminish after a minute or so of sanding, move down a grit and continue as far as 2000, below that you have a major scratch that will take a silly long time to fix with the tank full. as soon as the scratch starts to blend in to the surrounding area, cover the entire length of the scratch until it is no longer visible, and then move up a grit and repeat to whatever level you desire.
with the tank full of water, you will see slight cloud at 4000, and it will be clear at 8000. 12000 will make the acrylic clear when the tank is empty and dry, but hopefully you won't be looking at it in that state. if you ever empty the tank and want to finish the process, get a nice soft cloth and some novus polish... enough elbow grease and you will never know a scratch existed.
if you live near a detail painting/hotrod shop, you should be able to go in and if they are friendly you can get single sheets from them. total cost will be less than 10 bucks.
plan on spending a few hours by the way for a scratch that long if you want to go all the way to 12000.