I agree that the valve should be all the way open when splitting but not so sure about your figures on the heat factor. For instance in the neutral valve position there is 100% return to the tank against no resistance and that is not much of a heating situation, however coming to the end of the stroke on an open centre system forces 100% flow through the relief valve, yet no work is done but that will quickly heat the system.
Remember activating the valve builds up pressure, if there is a tough log to split and piston barerly moves.....count on high pressure. Pressure comes from the resistans, not from the pump.
If valve is only half open, half the flow move piston and half goes to tank, you will have 50% of energy in heat losses to tank....if relief valve opens .....like you say, 100% heat losses to tank.....
Very important when operating is to pay attention on piston, if it stop moving on a split-stroke, the relief valve will open and that will heat system very fast......
there is heat losses even in neutral....hopefully small...only way to figure is to measure P before and after valve with full flow..... its allways a good idea to have a permanent pressure gauge mounted direct after pump. that can help trouble shooting, and also help how to operate properly. A gauge is only about 25$ with fittings......
there is allways losses as soon you start the pump, the higher flow the higher losses. Manufactured woodsplitters can show "nice" numbers in specs but manufacturer cut costs with under dimensioned valves, hoses, and tubes, which creates resistance. That happens every where, even on 100K$-500K$ heavy equipment.
Example. a pump with 8 cub cm (0.5 cui) displacement and 3000rpm will give 24 litre per min (6.3 GPM), If max pressure is 20 MPa (2900 PSI) the hydraulic power will be 8kW (10.7 HP). If half flow goes to piston, 12 l/m (3.15 GPM) the other half will go to tank, 4kW heat to tank....if pressure is only half, 10MPa (1450PSI) its still 2kW heat to tank.....
Note:
hp = Q x P / 1714
where:
hp is horsepower,
Q is flow in gpm,
P is pressure in psi
thePower in kW is pressure in MPa multiplied with flow in litre/sec
10kW equals 13.4 HP
10HP equals 7.45 kW