Hi,
Wow, lots of stuff in series with the cells !
It's not just the cells, there are two diodes and a mosfet in series with the cells, plus a 1 ohm resistor.
The two diodes could require up to 0.8v each, and the 1 ohm resistor another 0.4v, so that's another 2 volts right there. So there is not much room for left.
The diode and resistor on the output consume power but they do take that power from the M317's so that's not too bad, and the input diode takes some too. So the dissipation of the LM317 is already limited to less than a watt.
Lets see, 15-0.8-0.8-0.4=13, so we are starting with about 13v or so not 15. 13 times 0.080 gives us 1.04 watts. So we end up with 1 watt plus a little more.
Now all we have to do is add a tree, a golf cart, and a pigeon coup in series with the 15v supply and we'll be all set. We've already got everything else so what the heck