It seemed sensible to replace the existing power supply with the scruffy old battery and keep it charged with the solar panel. The only problem was that the solar panel charge controller was [A] broken (sea water had caused a short-circuit and various burnt components), and [B] designed for a 110AH battery rather than a 7AH one.
Float charging of a lead-acid battery requires very precise voltage control and temperature compensation. Too high, or too low, float voltages damage the battery in the long term. It seems to me that there is a simpler technique for a battery which, even when old and damaged, has much more capacity than is needed for occasional 6 minutes bursts of 150-200mA.
Float charging from a solar panel either requires quite a complex switching regulator, or a linear current limiter which will dissipate several watts in bright sunshine, but simply connecting the solar panel (maximum current at midsummer noon approximately 800mA) to the battery through a diode and a MOSFET switch charges the battery effectively without any components dissipating significant heat. The solar cell and the insolation define the charge current without further electronics.
When the battery voltage exceeds 13.8V the battery voltage sensor (op-amp a) turns off the switch and allow the solar panel to go to full voltage (but no current) until the battery voltage drops below 13.4V when the cycle is repeated. Although this