Let's see..0.2V across the solenoid contacts at about 26A means it's dissipating around 13W in those contacts. That seems like a rather larger voltage drop (and power dissipation) than one would really prefer to have, particularly if there were a case when a higher current were flowing. Power dissipation is of course proportional to the square of the current (or the square of the voltage, which is saying the same thing), assuming a constant resistance.
It seems to me that there's still a rather substantial voltage drop you're not seeing somewhere. Maybe across the trimetric shunt (or more likely the connection between it and the house battery)? One would expect a small voltage drop (several mV) across the shunt, since that's how it works, but not three-quarters of a volt.
