Chris,
The 78xx series regulators are linear regulators. They do a great job but for the simple task of powering LED's, which don't really care if you get clean or crappy power, I suggest you instead get yourself some buck regulators. They work like switching power supplies and are very efficient compared to linear regulators.
As for use, keep in mind that the amount of power dissipated is based on the difference between the input and output voltages. The higher the input voltage, the greater the amount of power wasted and here's why:
Suppose you have 18v in and 15v out. That is a 3V voltage drop. Current is, for the sake of this example, an arbitrary 300mA. The amount of power dissipated will be 3V x 300mA or 900mW (ALMOST 1 watt). Now, lets say you upped the voltage to 27 volts. You now have 12V x 300mA (the current stays the same regardless of input voltage). So in this case, 12V x 300mA = 3,600mW. OMG, you are now wasting over 3-1/2 watts of power. As 9V batteries are quite expensive and have very low AH ratings, it's fair to say that the more power you throw at it, the more power will be completely wasted. In other words, because current remains the same regardless of input voltage, the greater the voltage drop required for your regulated output, the greater the amount of power dissipated. Also, to be stable, on these type of regulators, the input voltage needs to be higher than the output voltage. I forget how much but it's like 1.2 or 1.5 volts. That is the headroom needed. That means that you are always wasting some amount of power. I realize that you don't want to redo your circuit but for reasons of efficiency, especially when it comes to those LED's, it's best to plan the voltages required by arranging them in a parallel/series array so that a minimum of current dropping resistors are required. Or how about just rigging up 15v with AA or AAA battery holders? The pack will be bigger than the 9V batteries but those batteries are a ton cheaper and will last much much longer AND no regulator required! I'll bet you anything that even if you fed it 12v (8 cells instead of 10), that the LED's will still light and the difference in brightness might not even be noticeable. Saves you 2 more cells, less current consumed, and a smaller pack to boot. Try it, you'll see.
So with respect to your "new" project which requires a 3v regulator...... do you see where I'm going with this?