
So then I performed some calculations to see what we could do with 4" PVC to optimize the area. I calculated that even if I removed the paper cases (1.0625 inches to 1.0000 inches), I'd still be short room, but just barely.

Don't let the math scare you; this is basic Geometry. SOCAHTOA!!! In short, there wasn't a way to put 10 cells into a tube without cutting it as in the first picture in this post.
One of the greatest things about PVC is you can work it fairly easily. Simply heat your oven to 250 degreed (F) and put the tube in for about 5 minutes. This might sound odd, but trust me it's hard to fuck up. Longer won't hurt (it'll stay workable longer), but at some point it'll start to curl up like Shrinky Dinks; shortly thereafter it'll start to smell (it won't smell unless you get to this point). You'll need gloves. Also, PVC stays hot for a very long time because it's a poor insulator.

From my calculations, we maximize our design with a rectangle 2 inches by 5 inches. I first tried to form this with a couple of 2" boards and some handiwork. No dice. So next up I built a nice mold to force the PVC into a 2x5" rectangle.

Never underestimate the power of a stick of butter when sliding things onto each other. Grease up anything that makes contact with the mold, then grease up the mold. I once moved an 800 pound safe from my truck, up a couple of stairs, and into a closet with 2 buckets of butter and some boards.

Here's the PVC halfway on the mold. Note that there's no way to get the PVC off once it cools unless you destroy the mold or cut the pipe. This means we need to take the PVC off of the mold before it cools. Once the shape is formed, start sliding the mold back and forth so that you homogenize the diameter of the PVC. Then slide the PVC off, like I did here:
Once cooled, you can stand on the 3" long PVC and it doesn't deflect enough to damage the batteries. This is great because I want to put these battery packs very low on the frame, which means they'll be subject to the weight of passengers, cargo, falls, abuse, rain, etc. Once the batteries are contained, I won't need to worry about damaging them with everyday use.
Unfortunately, the 4" PVC is approximately 1/2" too small in the length direction. This is because PVC shrinks when you heat it up. To remedy this, tomorrow I'll repeat these steps with some 5" PVC... which doesn't come in the lightweight green. Note that I widened my mold by inserting a 3/4" piece of plywood. There will be two 24" long PVC rectangles when I'm done forming tomorrow.
On the connectivity side, i attempted to solder the batteries into parallel and quickly determined that I don't want to waste time with wire. Wires fray, are thick, and could short out if a strand breaks off. This could damage the cells, so I called off the soldering.
Instead of wiring with cables, I'm going to buy some aluminum sheets and cut out my own tabs to solder onto the standoffs on the existing tabs. I'll need to drill holes in the sheets to allow air to flow around the batteries. One of the cool things about using a tube is I can put a fan on one side and force air through the entire pack.