A couple of comments. One is the 3mA LED. That is small, but it will be burning all of the time even when you know that charging is happening. Instead, drop some teeny tiny switch in series with it. That way, you can push the switch button and see what you have, but then you release it and there is no 3mA drain.
If you are getting about 17V open circuit in a big solar panel, that is pretty good. As a general rule, only the fairly good solar panels will get you 17V, and many of the cheaper and lighter panels get you only 15 or 16V open circuit. I guess this thing you are doing now is aimed more for 7.2V.
Everything that I have done is with a big panel, so I think only in terms of nominal 12V, so I don't want to steer you wrong about this smaller scale rig.
I was trekking in Nepal, and I was eating dinner in a Sherpa lodge that was candlelit. The proprietor went into the back room and then carried out a 12V car battery. He sat it down on the table and set up a battery operated slide projector. After showing slides of himself on Mount Everest in 1972, he explained the problem to me. He had a good solar panel on the roof, but his charge controller had failed, so he was trying to do things the hard way. I studied it and agreed that it was a charge controller problem. So, when I got home, I ordered up a perfect-size charge controller, received that, and then sent it to San Francisco to his employer. They sent it over to Nepal in a satchel, he hooked it up by my diagram, and it worked. So, now they show more slide shows, solar powered.