in the conventional 1 part halyard case, the headboard load is taken entirely by the one part of the halyard. This turns around the sheave at the top of the mast which now must carry 2 times the load: the tension in the line going down to the headboard and also the tension in the line going down the mast to the deck.

In the two part halyard, the headboard load is the same. But it is split between the two parts of the halyard: the dead end, which goes up and is pinned at the truck, and the running end, which turns over the sheave and goes down to the deck. As you say, this same load, split between the two parts, results in 1/2 the luff tension in the line - same as any two part tackle. Therefore the pin at the truck that carries the dead end, sees 1/2 of the luff tension. Just as in the one part case, the sheave sees two loads: the line going down to the headboard and the other side going down to the deck. This line has the same tension in it as the dead end - it is part of the same tackle - that being 1/2 the luff tension. The two lines running over the sheave result in the luff tension on the sheave - not twice the luff tension as in the one part case.

I guess I will need to draw pictures?

One part case. 100 lbs luff tension results in 200 lbs compression on the mast:

Two part case. 100 lbs luff tension results in 150 lbs compression on the mast:

Now, you draw me a picture of what you think happens....