but might 36v from a pair of panels damage the actuator circuitry?
So here's the deal. Lead-acid batteries look electrically like a voltage source/sink with a small series resistance, with the voltage level a function of state of charge. 2V/cell (there are 6 cells in series in a 12V battery) is nominal, and if I remember right, their open circuit voltage is something like 1.9V empty, 2.1V full. That covers 90% of their behavior.
Considering that, the "1W@18V" spec of the solar panel isn't going to be able to "win" against the battery, and the solar panel's voltage will be pulled down to battery voltage, delivering probably 0.055A (=1W/18V) at whatever the battery voltage is.
When a battery gets completely full, however, its series resistance goes up dramatically, and the voltage goes up, until there's enough voltage to start electrolysis of the fluid and you get H2 and O2 generation at the terminals and loss of the electrolyte. A lead-acid battery, depending on the type + manufacturer, has a certain recombination rate of H2 + O2 => electrolyte that it can handle; if you electrolyze at a higher current than that, it leads to permanent electrolyte loss (+hence capacity loss)
So there is a safe current that can be delivered to a lead-acid battery continuously, where its own self discharge due to electrolysis balances the charging current. It depends on the manufacture + construction. I wouldn't feel worried about a C/10 or C/20 rate of charge (where C = the current needed to discharge a battery in 1 hour). Garage door batteries are probably > 1Ah capacity so you should be safe with 55mA charging current.
HOWEVER -- I would probably put a (zener diode and resistor in series) in parallel with each battery, the zener diode being about 14V and resistor being maybe 10 ohms or so, so that it keeps the battery terminals from getting charged too far.
Also: if you can, wire each solar panel to each battery (and keep the diodes), rather than the pair of panels in series wired to the batteries in series -- i.e. try to connect the center taps. By doing so, you'll charge each battery independently. Otherwise, what can ruin battery life is if the battery voltages diverge -- the one with the higher voltage will tend to get overcharged, while the other one will tend to get overdischarged and not completely charged.
There are a number of issues here. In no particular order:
The solar panels should each have their own series blocking diode. If one solar panel is covered and getting partial shade, its output will be less than the other panels and will be a power sink instead of a power source.
The solar panels deliver 4.5V at 80mA at full sun. Under partial sun they won't deliver enough voltage to charge the batteries.
The rechargeable batteries have a voltage of 1.2V, not 1.5V. This means your battery bank has a 3.6V output, not a 4.5V. This works to your advantage as the LEDs will still work (typically from 3V - 5V), and the solar panels minus the diode voltage drop is still enough to charge the batteries under full sun.
Rechargeable batteries like this need to charge at a rate of 10% of the aH rating for 16 hours, for a total of 160% energy in to get 100% energy out. You may need to let this charge for 2 full days to get the batteries to full charge, under full sun.
Given that, will the system charge and discharge correctly? Under full sun, yes, your system will work as expected. The light output may be a little lower than if you were running off of non-rechargeable batteries, but not enough to notice.
Will the lights be powered with the correct voltage and current? Yes. These types of LED lights are designed to work with 4.5V of non-rechargeable batteries and will provide light down to about 3V. By staying just under the engineered voltage for the LED lamps, you are not likely to overdrive them and still achieve an acceptable amount of light.
Best Answer
You need to know the short circuit current and open circuit voltage of your solar panel to be able to tell for sure, but NiMH is a good option here since they self-limit any oversharge well given that the current is low enough, and at 80 mA, it should be. NiCd is even better in this regard, but they are terrible otherwise. If your open circuit voltage is much higher than 1.6 V/cell, I would at least think about it and test it first.
Perhaps you could put a bit less stress on the batteries by using an LDO like your suggested LM317 to limit the peak voltage. If it's a one-off, I would not bother. If it's mass production, you need to find and test the worst case scenario in this regard and check the datasheet of your batteries.
Normal NiMH charging is done with either negative delta V detection or temperature sensor to terminate the charge. The former is possible in your case but the current is too low for the latter.
If you want to keep it simple still and limit the voltage and balance the cells, something like this would be a safe bet. 1.5 V Zeners don't exist, hence two cells in series per Zener (~3.1 V):
simulate this circuit – Schematic created using CircuitLab