Viability of an LED grid

Well, let's analyze the circuit. We know that the power required in a DC circuit is:

P = Vsrc * Iout

We know that

I = (Vout - Vled)/R

and the power delivered to the LEDs is all that matters, so we want to maximize

Pr = (Vout - Vled) * I = (Vout - Vled)^2/R
Pled = Vled * I = Vled * (Vout - Vled)/R

Clearly, we want to minimize Pr and maximize Pled. We can do this without decreasing the current by reducing R and making Vled close to Vsrc.

This is accomplished by putting the LEDs in series.

However, your battery (isn't the 6LR61 a 9V battery?) will go from some nominal voltage (ex 9V) to a lower voltage - 9Vs are spec'd to be dead at 4.8V. This means that a passive solution will go dim while there's still charge left in the battery. For your original schematic, that might mean that you'd end up below the minimum current to turn the LED on, or for the series version, the voltage might go below the diode forward voltage.

A simple way to extract more brightness with the same power is to pulse the LEDs - Human eyes percieve blinking light to be brighter than continuous light, even if the average power is the same. A 555 timer or other oscillator/switch combination will be able to do this, no microcontroller required. Try playing with the duty cycle and frequency of your LEDs to see where it looks the brightest - You may be surprised!

Also, a switching power supply can increase the efficiency of your regulation circuit to 80, 90, or even 95%. However, that will drive up the cost and complexity of the design, and may not be necessary.

Plenty of cool white (and straight UV, if you like) LEDs are available (and the cool types actually have better lumens-per-watt efficiency than the "warm" types, as a general rule.)

Lumens-per-watt efficiency is all over the map, so you have to check the particular LEDs you are considering using. Some are awful, some are quite good.

Cooling is something you'll have to sort out, especially with high power LEDs, where thermal design is most of the design work. Stock aquarium hoods are terrible for it, so most folks with serious lighting setups end up building something that allows the lamps to cool more effectively (may involve a fan, may involve a barrier between the water and the lamp which will slightly reduce light into the aquarium, but greatly reduce humidity at the lamps, etc.)

One factor you may have missed is that the LEDs drive all the light towards the water, where the florescent has considerable losses from the parts of the lamp where light is reflected before hitting the water. I have 8.9 watt LED ceiling fixtures which are undeniably brighter than 13 watt CFLs for exactly this reason, even though they are "only" 70 lumens per watt.