Wood – How plausible (and how hard) is it to modify a billy bookcase to fit a gable-end corner, floor-to-ceiling, with an impinging 45deg roof

Plywood will not sag over time if you intend to use it for the door faces. I recommend birch plywood for not only its hardness but looks. However your hinges and what they are attached to are the big concern in this project. It looks like you've used a low grade pine to build the unit. This is a soft wood and a couple of cabinet hinges screwed into this are going to loosen quickly. Your best chance for longevity is to use a piano hinge so that you have a continuous hinge from top to bottom with 15 screws or more on each hinge. I highly recommend ordering a stainless steel or flat nickel piano hinge for this. What they have in stock at the box stores is of the "bright" variety and looks cheap to me.

I'd also recommend that you not attempt to build the door to be perfectly flush with the "lip" at the bottom. Leave yourself 1/4 of an inch gap. Units like these always sag at least to some degree and you wind up with the door scratching the "lip" and its going to look really bad with time.

Also take a look at ball catches to use either at the top or bottom of the doors to hold them in place once closed.

While I am not a cabinet maker by trade, I have successfully built two full sets of cabinets (base and uppers) and am currently getting ready to hang my third in my newly renovated kitchen.

First, always start with the corner box. If it is not already level, square and secure, you'll want to make it so before attaching the other boxes as it's your foundation.

For #1: Yes, you will clamp the front frames together to align and level them to the corner box. Then secure them to the wall using #2 answer below. Then you need to attach the frames together as that will keep your seam from becoming a gap. Your screws need to be 90 degrees not angled when you screw the cabinets together. Do not glue, you may want to replace or refurbish later. You can easily hide the screws by counter sinking your screws 1/2 inch or so and using a plastic or wood plug. Or simply use a nice brass finish screw to compliment your woodwork. Or use a screw that blends in with the color of the wood if you are really concerned about it. Since your cabinets will be painted simply paint the screw head if it is even visible.

For #2: In all of my cabinets I have built a 1 x 2 solid wood rail at the top and bottom of the back of the cabinet that the 1/4 inch panel is nailed. I use this to attach the cabinets to the wall studs for base and upper cabinets. I use 3 inch drywall screws. You do not need to secure to the floor unless you are creating an island that does not have wall access.

I have not tried them, but you can also purchase rails in 8 foot lengths that you can hang on the wall, then attach brackets to your cabinets that hang on the rail. This secures the top of the cabinet but I'm guessing you'd still need to fasten the bottom through a stud.