Stu your diagram and logic look about right, logic and engineering are not mutually exclusive, you just need to be careful when you simplify things to keep the important things and get rid of the unimportant.(hopefully I am doing this but I could be wrong)
To simplify the analysis I think it is best think about the joints between sections of the stump as pinned joints i.e. they will flex also think about the hull being very flexible.
The simplest is a boat with no stump and a perfectly straight mast , when you put the rig tension on the sides of the boat will flex up and in slightly. As this happens the distance from the shroud points to the gooseneck will reduce. If you had solid lowers, then the gooseneck would be pushed forward.
With this setup the only additional stiffness that the stump provides for the boat comes from the joints between the lowers and the stump (very little) and the stump to hull and spine connection. If the stump is about 1m from the deck connection to the gooseneck, then it either needs to be a large diameter, or very heavy to give you enough stiffness to make a difference.
Now think about having the stump angled back a long way, the rig tension puts the solid lowers in compression, and they press down at the shroud points forcing the sides of the boat down and out, this balances the up and in from the shrouds, and the boat is stiffer. The kicker loads reduce the effectiveness of this which is why the stump needs to be angled back further than you might think, and calculating the best angle would be extremely complex.
If you are using the stump to make the boat stiffer, then for it to be a gain you need to get back the of the extra weight of the stump and lowers back by making other bits lighter.
To summarise
No Stump ==> Bulkheads need to resist all rig loads
Free standing stump ==> Bulkheads need to resist all rig loads minus stiffness gained from stump
Stump with solid lowers that go into tension ==> Bulkheads need to resist all rig loads minus stiffness gained from stump and tiny bit from joints.
Stump with solid lowers that are always in compression ==>Bulkheads need to resist all rig loads minus stiffness gained from stump and minus compression of lowers acting at shroud points and a tiny bit from the joints.
It is worth noting that when you use a stump you get stiffness from the stump to hull joint, however you lose stiffness from the mast below gooseneck to mast above gooseneck joint.
Carbon is stronger in tension than compression but the stump to lowers joint, and lowers to hull joint is complex, can you be sure to get the full benefit of carbon's strength if the fibres are not lined up properly through the joint. There have been a lot of broken gantries because joining small tubes together at acute angles is difficult to do.