What's going on with this switched outlet wiring in the middle of a run?

Question

Help me figure out what's going on here and come up with a way to turn this into a half-switched outlet?

I have a late 1940's house, and some of the circuits are not grounded. I recently replaced all of the switches and outlets in the house, putting GFCIs in the first receptacles on each of these circuits to protect the ungrounded outlets.

While I was doing this, I thought I'd change some of our switched outlets to be half-switched. The first one I did this for was on the end of a run, so it was pretty simple because there was just one cable running from the outlet to the switch. But the second one was in the middle of the run and is set up in a way I don't understand.

Here's a diagram of the outlet and the switch:

The switched outlet has two wires connected to the neutrals and one to the hot. One of the wires connected to a neutral (D) is hot whether the switch is on or off. If I disconnect this wire, none of the outlets further down the run work, so that's definitely my hot line. The neutral from D's cable (E) is connected to one of the three wires from the other cable in the box (C). The other two wires from that cable are connected to the outlet, one to the hot and one to a neutral.

In my switch box, I also have a 3-wire cable, which I assume is the one from the outlet box. One of the wires is directly connected to the switch (1), one is connected to a wire from the other cable in the box (3), and the third is connected to the other wire on the second cable, with a pigtail to the switch (2). Whether the switch is on or off, a non-contact voltage tester beeps at the wire 3/5 connection, so I'm thinking that's what's carrying power to the remaining outlets in the run.

Two questions:

1. How do A, B, and C line up with 1, 2, and 3? Seems to me like C/E are neutrals, connected to 2/4, and A/D are hots, connected to 3/5, which would leave B as 1, completing the loop for the outlet.
2. Is it a problem that there's a hot wire connected to a neutral terminal on the outlet, and how should it be instead? Maybe A/D should be attached to the hots and B to the neutral?
3. Is there a way to make my outlet half-switched with the existing cables?

Answer 1

Did not ultimately get a lot of help here, but I figured it out myself, so posting in case there are others who run into a similar situation.

The first key was figuring out how the wires in each box matched up. I connected D, the hot wire, first to A, then to B, which helped me figure out which two wires in the switch box they matched up to. C I knew was the neutral, so it was the third wire; whichever one I didn't hit by hooking D up to A & B.

Then I essentially did this:

• Knowing that D was the hot coming in and G was the hot going out, E was the neutral coming in and F was the neutral going out, I figured I had to connect the two of those
• Realizing that I had a third wire, B, in my cable from the outlet to the switch, I determined I could use it as the second hot for the switch

So the top outlet is switched, the bottom is not, and I no longer have hots connected to neutrals, which to reiterate, is how I found it, not how I chose to wire it.