External UV light (inside hood)

this will also probably kill of any fish and other living things in the tank..
and possibly harm your eyes as well.

This seems like a dangerous way to attempt to sterilize your water.

High UV exposure is carcinogenic. This is the reason why it is a good sterilization method. It basically introduces errors in the DNA / RNA replication process. This happens for bacteria, plants, fish and humans. There is a reason why uv units have a housing.

In order for the UV dose to be enough to sterilize water you need low flow and proximity.

So bottom line this setup is not only ineffective for treating algae in a functional aquarium but it is also dangerous for your health.

UV is also radiated by the sun and reaches our skin at low levels. Indirectly, it is the reason why we tan. This low dose of UV can be mostly dealt with by our natural DNA reparation mechanism.

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Sounds like a "pile on" day for the idea?
But I do have to agree that the idea may have some flaws. As I see it, you will not be exposed long enough to do much harm but then I doubt there will be much good, either. Water is difficult for the UV to penetrate very far. I using UV to make "found water " safe to drink, the water has to be exposed to the bulb very closely and for something like a minute. Murky water will totally block the UV so the water has to be clear to get it to penetrate even an inch. I doubt that enough will penetrate for long enough for much progress.
But then to avoid totally bumming the idea, I do see a good start on a DIY light system that can be very easy to adapt to different uses by changing bulb size and type.