I can't answer the question your asking. BUT I can say their is absolutely no way that you could talk me into cutting that tank down. I might sell it and buy what I really want and pocket the profits. But I'd never cut that down.
I do not know from experience but from what I understand about acrylic the top of the tank is very, very important part of the tank, structurally. I think it could be done, but the acrylic would have to be extremely thick to prevent bowing, and eventually structural failure. 1" is very thick for a 180g tank though if cut short enough it might work.
The tank looks like it is in good shape why not sell it and buy a rimless frag tank that was designed to be that way?
A router would be fine and should cut through it. I have used a router to cut acrylic of different thickness before (depends on the piece I have), the only issue I had was it was hard for me to keep it straight. I could cut it but I had trouble keeping it perfectly straight (the pieces I was cutting were meant for practice and were scrap we got for free). Then again I am not a tool person and I would not say that I know what I am doing but I would test it out on a scrap piece first if you can get one so you get used to it.