... If I am correct, then which of these operating point targets should I try to achieve to emulate the Marshall sound ...
We're not there yet.

Sorry for the absence, but I'm working on getting a job.
Regarding the loadlines/cathode lines:
Step back from it for a moment. The graph is just a visual way to describe all the possible outputs if you change a variable, just like graphing an equation in school. The plate loadline is easiest to grasp because it will be a straight line; this line describes a resistor, and how ohm's law spits various values of current (y-variable) with changing values of voltage (x-variable).
Now think about the resistor itself: one end is tied to the supply voltage. Pretend that the opposite end also gets attached to the supply voltage (let's say the voltage is 300vdc). If both ends are at 300v, there is zero difference in voltage between the ends, and zero current. You plot a point at 300v, 0mA.
Let's also say our resistor is 100kΩ. Let's say the side not attached to the supply voltage is at ground potential (like the tube is shorted from plate to ground). The value of current is solved by ohm's law, 300v / 100kΩ = 3mA. So you plot the 0v, 3mA point. Connect those 2 points together, and you get a 100kΩ loadline for a supply voltage of 300v.
Now the bottom-left corner of the graph is the origin or 0v, 0mA so why don't we have a point at that location? Because the non-varying end of the resistor is pegged to the supply voltage. The varying end is attached to the plate, and the values of voltage shown on the x-axis are tube plate voltages. So the plot of phm's law using this resistor move up and to the left.
The cathode resistor, however, has an end connected to ground. So 0v, 0mA will be a point on the curve for the cathode resistor. Notice I said
curve. The graph is nice & square for plate voltages and plate currents. However, the cathode loadline uses plate current (which for a triode will be equal to cathode current, and therefore current through the cathode resistor) and
voltage drop across the cathode resistor, which is the same as grid-to-cathode voltage. These voltages are not shown on the x-axis but by the grid voltage curves. As you found, you have to plot the value of current when a voltage equal to the grid voltage curve is dropped across the cathode resistance.
And where the 2 lines cross is your idle point of the stage.
The perfect cathodyne, 240V supply, could swing 240V/4= 60V peak.
Again confused... are you making a general statement about the perfect cathodyne? That is, a perfect cathodyne can swing 1/4 of the supply voltage.
Maybe you've moved beyond this, but I'm back-tracking a bit.
I don't have any memorized rules for phase inverters, so I looked in RDH4. Ch 12.6 ii (A), pages 522-523, it says it is normal practice to assume the maximum grid-to-grid output of the split-load/cathodyne/concertina inverter (which RDH4 simply calls "phase splitter") is 1/4 * supply voltage, peak-to-peak.
A run-of-the-mill common cathode gain stage can likely swing an output at least 60-75% of its supply voltage, depending on plate load and idle point. A paraphase inverter is basically one of these gain stages, and a 2nd one with a voltage divider in between to knock down the signal to the 2nd stage. The result is 2 outputs with similar size and opposite polarity.
I did not see any obvious rules for a long-tail inverter, or its root form in RDH4, the "cathode-coupled phase inverter" (Ch 7.2 viii (A), pages 347-348). What I
do notice is that some amount of voltage must be dropped across the tail, and the bigger this voltage, the better the balance of the inverter. Within this guideline,
Aiken and Merlin (
d.c. and
a.c. versions) basically calculate the stage as though is were a common cathode gain stage, except they go back to estimate the amount of imbalance and how far to trim plate loads to restore balance.