Electrical – Splicing 6/3 wire to multiple 8/3 wires (or even other 6/3 wires) inside a junction box

The receptacle manufacturer should document how many wires can be put where. In general, if there are screws, you can use at most one wire per screw. For quickwire/backwire holes, you can only use one wire per hole, and further, that one wire can only be 14 gauge. Previously, 12 and 14 gauge were allowed for quickwiring, but not any more. The only kind of receptacle where you can directly attach a whole bunch of wires are those where the screws tighten down a bar onto another bar. Then, you stick stripped wires between the two bars and tighten the top one down to clamp them between the two bars; you can run quite a few through there.

Another limiting factor is box sizes. Boxes have a fixed wiring volume, and there are rules for working out the minimum volume box needed to accommodate a given number of wires, devices, and clamps. Assuming you're working with 14 AWG grounded cable, I'd expect the box to accommodate 4 hot + 4 neutral + 1 device + ground wires, so 10 wire volumes, and 14 AWG is 2 cubic inches per wire, so you'd need a 20 cubic inch box. That's a bit on the large size for a box holding a single receptacle, but there are boxes and box configurations (box + mud ring) that would accommodate that many wires, so it's not unreasonable.

As for wiring everything together, you should pigtail everything and then hook up the pigtails to the receptacle. The pigtail presents a single wire for slipping under the screw terminal. Remember to wind the J-hook you'll slip around the screw in the direction that you'll turn the screw to tighten it, so down on the left side and up on the right side.

This family of lights uses all 120v wiring which means the full weight of NEC applies. You cannot "freestyle" splices in the manner you are talking, you must use listed products, which those cheapie butt splices probably won't be. They do exist, but O'Reilly Auto doesn't sell them and they don't use $5 crimp tools either.

So here's how you handle "the cord is too short". Legally, splices can only be inside junction boxes. The American gold standard way to splice inside a junction box is with "wire nuts" - for two 18ga. wires I would use the blue or gray ones. Do not use stabs, they are not rated for 18ga.

If GE sells a listed method to attach their special connectors to your lamp cord, go for it. Otherwise you can only use it between junction boxes, which means 2 junction boxes. If you want to do it in one junction box, then buy 2 cords long enough to give you 8" slack inside the box, and splice there.

But I have to say: why on earth are you using this family of products? Don't get me wrong, GE's quality is first rate, but why wrestle with 120v products when you can get the same thing in 12v that's much easier to work with.

Also, these prices are way beyond insane, at least 3-4 times what I've seen in quality 12v products. IKEA has a broad selection of 12v products at sensible prices. 12v makes the products cheaper because they do not need expensive voltage converters in each lamp. I buy cheap Chinese LED strips for $7 for a 16 foot roll, I mention that only to shake you out of a notion that $60/foot is a normal price for these things.