well when i first started reading this post i said hey i wonder if hydrocloric acid/ muratic acid would clean that tank up and fast and easy after all coraline algea is basicly lime based. and it's kept in plastic bottles and shouldn't effect the acrylic but i guess it's too late. Being a General contractor and very handy, i would recomend that you not even try to buff out the front glass, if what we see in the pics are scratches and not scuffs it's not worth it, evn if you get rid of the scratches for the most part the amount of buffing needed in one spot over another wil creat what i'll call bottle glasses efffect your view will be distorted in one spot / magnified or blurry. my sugestion to you would be to by a new piece of plexi glass and Cut off the front piece. It's not that hard to work with plexi glass but there are tricks to it. The internet is a great place google cutting and soddering plexi glass/ acrylic.
good luck