How To Turbo-Charge My LED Light String

I am new to electronics, but I have an idea and hope that it’s simple enough for some of you with more experience can tell me I’m either on the right track, or complete wasting my time. I have looked at a number of basic solar light / charger circuits in here and on the Web, and have a very basic grasp of how they work, but the intricacies and exceptions are still fuzzy to me.  I don’t want to recreate the circuits, and want minimal soldering since I’m new to that too.

I have a 40 foot long string of 100 LED solar lights that are driven off of one hard-wired AA Ni-MH 1200mah battery.  There are three ideas I have to supercharge the string to improve it.  Without tracing through the existing circuit (which I may not understand anyway), I want to draw on your experience before I get too involved. If I ultimately need to pull things apart and try and trace the circuit, I will, but until then, your guidance would be appreciated. I would like to:

A) Remove the old battery and add a larger capacity battery since I currently get maybe three hours of light.  Probably easily done.
1. Changing the battery to a larger capacity looks straightforward.  I will be adding a D cell (if it fits the case) NI-CD with 3000-5000mah (not purchased yet).  Since the cell is the same voltage, can I assume that the swap doesn’t really affect the circuit?

B) Add another solar panel.  Probably easily done. 
1. I have one small solar panel that came with the unit which feeds the existing battery.  I am assuming that it is 2v (to suit the AA battery) and based on the size, I am assuming that it is between 100 and 150ma peak output.  I would like to add another small panel that I have lying around that is rated 2V / 150ma.  Installing these in parallel should give me a higher energy input, but still at the 2v. Looking at the circuit board the solar panel goes to the board before the battery.  I am assuming that the only thing between the solar panels and the battery is the diode, and that there isn’t any sort of current / voltage limiter on the board.  Can I assume this? Is the diode likely to handle me doubling the power through it?
2. My calculated peak solar power for the two looks to be about 250 to 300ma.  By following the 10% rule for charging and assuming that I’ll likely not get 100% rated solar power for long,  I’m assuming that I my D-cell should handle the trickle charge?

C) Increase the power through the white LED’s.  This is my main question, and biggest uncertainty.
1. I am assuming that driving 100 lights off of one battery does not really get close to the maximum.  I pulled the shrink tube off of one of the LED’s and it appears a simple parallel connection.   I don’t see any resistors that are inline with the LED bulbs or directly before or after the LED string wires on the board. I’m assuming that I can add a resistor in series with the light string. Will the light output change much? How can I figure out what resistance to add without blowing my LED’s? Am I on the right track?

With my very rudimentary (and possibly wrong) multimeter skills, I tried to find the following as well:
Battery voltage – 1.16 v
Voltage (measured as parallel with the light string) – 2.56 v
Current (measured in series with the light string) – 13.1ma (this sounds low?)

I’m slowly learning my way through this, and I want to put together an ‘ible together when I’m done.  Any help, corrections to my assumptions or suggestions you have are appreciated. Sorry for the long-winded message.


Picture of How To Turbo-Charge My LED Light String
My previous post appears to have been lost somewhere, again, so here's a quick answer:

A- as long as the voltage is the same, you can use any capacity.

B- panels in parallel will just raise the maximum charging current. you want a slightly higher voltage to charge more.

C- resistor drops voltage, so LED's will be dimmer.

Note: Battery voltage with no load should be >= voltage across load. 13mA for a single LED is reasonable, but is very low for the whole string.