Electronic – What’s the third footprint pad on some SMD LEDs for

If you're interested in solderability and manufacturability, then you should follow the recommended pad layout. I've never had a manufacturer's recommended pad layout give me grief, although I have run across a few vendors whose dimensioning requires a fair bit of headscratching and pencil-and-paper chicken-scratching in order to figure out offsets and spacing.

You are making some bad assumptions in your calculations though. No, pins are not often centered on the pads "lengthwise" but they are often centered widthwise. Y1 and C1 would most certainly be given by the manufacturer. The recommended land pattern will (in my experience) give more space for the pin on the "outside" of the pad and less underneath it. My guess is that that gives a good shape to the solder connection. You won't have anything in terms of heat dissipation unless there are a lot of grounds or you have a ground pad underneath. In the case of a lot of ground pins, you'll want to give them a lot of copper fairly quickly, but you'll want to connect the pad to the copper with thermals or you'll have soldering problems.

I wouldn't worry about minimizing board space, especially if you're not building a million of these. The half a millimeter you might save by shaving Y1 a little isn't worth it.

If you don't want the leads to protrude on the bottom side you essentially want to mount your TH components as SMDs. So I would suggest to use SMD pads, push the leads onto the pads, and solder them there.

For large/heavy components this might give a mechanical reliability problem: a round wire soldered at both sides (or soldered at the bottom only but with a component immediately at the top) can't easily rip the copper from the PCB, but a lead soldered to an SMD pad can!

PCB material is not optimized for conducting heat, so you might want to put lots of via's in the appropriate places to conduct the heat.

I read in your edit that you want to do this for trough-hole screw connector blocks. My gut feeling is that this will seriously impact the mechanical reliability. You could consider using those two-level connectors for screw terminals, which would free room so you could put your heatsink under only a part of your PCB, leaving the area of the screw terminal terminals to be soldered at the bottom.