Solar power - part II

I had some plans for the weekend, but unfortunately my wife's computer needed some attention, and I have spent most of the weekend replacing the mainboard and then getting the whole thing up and running. In the end, it looks like a monitor problem, so my whole effort was pretty useless. Anyway...
I was lucky to get some direct sunlight today around 11AM, and I quickly hooked a 10W white LED directly to the two panels in series. The LED clamped the voltage to 8V, making the panels operate way below their sweet spot, but I still managed to draw over 300mA out of them at max. That's almost 2.5W, which isn't bad! Even with some overcast, the current dropped to around 30mA and staying there.
I moved the panels to the balcony where they won't be in danger of falling down (they were origially sitting on the window ledge), and I attached a four wire cable to them, extending the both solar panel terminals to my desk (they're two 9V/5W ones). This gives me the opportunity to connect them in parallel and see if they perform any better.
I've seen some simple, NE555 based MPPT solar booster that I might try. That one charges 12v lead battery which I don't have, but that wouldn't be a problem. I would try the booster even without the battery, but... I dont have any NE555s. No kidding. I might find one in my UV-light PCB exposer timer, but I'd need two NE555s anyway.
The other way would be to go the supercap way. I am more and more leaning towards the idea of getting some 2.7V or 2.5V supercaps, and using a nanopower booster to get 3.3V out of them. That way I can drain them down to something like 0.9V at least. My idea of charging the 5.5V supercap to 5V and then using LDO to get 3.3V out of it would simply waste too much of remaining energy. More than half of it would be unusable!
I know, comparing 12V, 5Ah SLA battery with something like 10F supercap is strange... but keep on mind I am just experimenting without having any goal. I want to be able to power one sensor node with the whole thing, which means I need 10mAh per day in the worst case. But, if I could get the SLA battery charged, I could use that power for something useful... charging my phone, letting RasPi running from it, or something. The only problem is - where to keep the battery? I don't feel good about having something that nasty sitting in the living room, and leaving the battery on the balcony would mean exposing it to wild range of temperatures. Anyway, that's a distant future, let's focus on the NE555 booster first.