Oh, but as for building a plexiglass frame...
You will need to build it in layers. Picture the tubes of a regular bike. When you remove all the components, the metal frame can sit nearly flat on its side. This is the shape you'll need to cut from the plexiglass. The "tubes" will need to be wider than the typical metal frame tubes, because plexiglass isn't as strong. You will need several layers of plexiglass, maybe 4 or 5, sandwitched together and glued with epoxy. You cannot use superglue because it will shrink when it sets, and warp your frame. Also, you may need a vacuum chamber for curing the epoxy, to draw out any bubbles that will compromise the integrity of the frame. Some parts of the plexi frame will need to be braced with strips of steel, basically any place you will be attaching a component. You may even want to layer the steel supports in with the plexiglass panels, then run several bolts through the layers. If you do use bolts, use a few of them, and make sure that they are spread out so that they do not create a pressure point on the plexiglass.
It will take many, many steps and lots of waiting to get this thing right. But if you do it right, and pay attention to where the pressure points will be, I think it could be done.