How to Convert 20,000 Lumens to Lux

Cutting the Alu in half and sticking it to the back will do almost nothing to help. What you need to do is increase the surface area of the Alu.

If you're stuck for space, then you have a couple of options. If you have space in the vertical direction, you might try just bending the alu so it's not as wide and fits into the shape of the available space. However, you do still need to make sure the heat can get to the outside world. There needs to be some kind of air flow, preferably over the alu.

If there is a fairly constant trickle of water to the plants, then you can use this to extract a lot of heat from the LEDs. Instead of using a sheet of Alu, use some box section. Seal up the ends and attach a push-fit pneumatic connector at each end. Pump the water supply through this, and you should be good to go. Even a tiny flow of water should be enough, but it probably needs to flow fairly constantly, not just once a day.

Astronomers, including amateur astronomers, are interested in the brightness of the night sky, and there are various inexpensive solutions.

There's a project to monitor the night sky using EURO 100 light meters based on PV solar cells (only available to participants).

There's a commercial device that is based on (I think) a Taos sensor. Around the same price. Calibrated in visual magnitudes per square arcsecond (logarithmic).

Even an iPhone app that uses the camera (not sure how well that works).