I could go on at length about this subject as I have looked into building both an aquarium and a print washer from acrylic and have even done some small projects that didn't look like his BBQ but easily could have. I finally decided to buy a used aquarium and a used print washer because it was actually cheaper and would look better.
Acrylic is not cheap especially when you figure out the quanities and grades needed. All plastic is not equal despite looking the same and working it requires some precision and holding jigs in order to use the proper acrylic glues. It is do-able but will cost about half of retail and can easily rival Homer's work.
But if you decide to go for it I can dig out some sites for you to look into.