I'll offer two approaches in this answer, a more-complex one based on a structure that I have actually helped build, and a less-complex one that's more speculative.
I have not actually built either of these as a sukkah; I'm drawing on related experience, but you'll need to do some work yourself to get from this to a plan for a finished sukkah. With luck not too much work for option 2, but use your own judgement.
Option 1: The ambitious small building
I do medieval/renaissance re-creation, and we have a large annual camping event. My camping group decided that we didn't want to use canvas structures for our food-prep area because of fire risk, so we built take-down wooden structures. These plans for a 10x10 structure are fairly detailed. Note: the parts labelled "FS" and "middle rail" are purely decorative and could be omitted.
You would need to make the following adaptations:
Forget about the rafters and roof; you're not putting a peaked canvas roof on it. I recommend instead getting several 1x2s or 2x2s (depending on the weight of your s'chach) and laying them across the top, like the kits from the Sukkah Project do. Their velcro fasteners are a useful approach, or you could screw them in or tie them down with rope.
Where the plans show cut-outs for windows, use solid pieces instead.
The walls for ours fold down into 6x6' sections, which is bigger than you're looking for. Every hinge is on a corner and I would recommend preserving that approach, but there's no reason you couldn't use more, narrower wall segments -- the assembly mechanism doesn't change, just uses more parts.
Instead of the corner post with openings on each side, you'd want another wall segment on one side and a door on the other. A door in this case is a wall segment that is (a) not screwed in at the top and bottom and (b) attached by hinges to an adjacent segment. (See note about door height under option 2; it applies here too.) I admit that I am doing some hand-waving here; use these plans as a starting point, but you'll need to think about door placement.
Our structure is a 10x10 square. We adapted these plans to also make a 10x15 structure; the difference in complexity was due entirely to the roof supports, which you don't care about. However, any given instance of this design isn't easily swappable for different sizes the way, say, the Sukkah Project's kits are.
If you make this (including the decorative half-timbering) I suspect you'll impress the neighborhood with your chiddur mitzvah. But this is a big project for which you'll want some power tools, so allow me to also suggest:
Option 2: Adapting the Sukkah Project's sukkah
The Sukkah project gives you a frame already, so if you start with that you just need to add solid walls. Since your frame is wood, this means you can use screws to attach walls.
Unless you are in a high-wind area, I would make the walls out of quarter-inch plywood because it's light and less expensive than 3/8". Don't use luan; that doesn't stand up to either wind or being stored vertically unless you reinforce it. If you anticipate trouble with wind, you can use thicker plywood.
If you do not want to carry 4x8 pieces of plywood, you can cut them lengthwise and use a piano hinge to attach the two halves. A piano hinge is a long hinge that opens completely flat but can be folded (like any hinge). I don't know if piano hinges come in different sizes; the one on my hammered-dulcimer case (yes, really :-) ) is between three and four feet long. That ought to stand up to use on an 8-foot-high wall, but if you're concerned you could use two of them.
The Sukkah Project's wood-frame kit uses 2x4s at the top and bottom for all sizes larger than 8x8. You can attach your plywood there with wood screws; use a drill to set screw holes every 1 to 1.5 feet, and then during setup screw the plywood to the frame. (You can use a drill on low speed for faster screw placement.)
This leaves the door. Personally, I wouldn't make a wall-height door; an 8-foot-high door is likely to be a bit of a pain to open and close. But you have two posts and a header frame at the opening for the door, so you can screw on a "lintel" piece at the top and then make a more-normal-height door. The door is attached to one vertical support with hinges (use screws so you can take it apart). For the handle, I would drill a hole in the plywood around doorknob height, run a rope through that and tie it into a loop (with some slack), and place a hook (or a nail) on the vertical support on the inside. Pull the door shut holding the rope, then drop the loop over the hook to keep it from opening on you. If a child manages to trap himself inside, in the worst case you cut the rope from the outside and push the door open. (It is conventional for doors to open inward, but with the frame design shown on their web site there's no particular reason you couldn't put the hinges on the outside if you prefer.)
These walls/door will not be 100% airtight; the pieces abut each other but do not overlap and are not caulked, after all. It's a temporary structure, not a building. But it should be good enough to have a pleasant meal on a windy night, and if the weather is too bad you're going to have problems overhead anyway.
