The power supply isn't really a major problem, you can incorporate into the design a set of battery's that would be constantly charged, when the power is available, and would be used when gone - providing power for XX hours. It's a matter of design criteria. Others for example would be - the operating temperatures (it would need a heating unit to work in freezing conditions). Intensity of lights at given distance. number of lights, their angles, angles of overlapping (if needed) etc. etc.
The lights dimming would be for the device itself, not for the platform, as you can produce some insane amount of light with todays LED arrays. With enough units, you can make it brighter than your landing lights. The high intensity LEDs usually produce light in 110° cone - in this case, the led would be visible on 110° horizontal, and given focused amount in vertical. Let's say a the glidepath would be 10° wide - you can easily focus it that way using a lense. So, using an ring array, with 24 LEDs, in any given moment there would be 7 hi-power LEDs visible to you, more if more rings is used... so, look at the modern strobes, and imagine that such ODAPI device would look to you as 24 such lights at once, non-stop. That's a lot of light.
Using GPS or radar return to deterring the CTB can be also used, although I thinks its application and accuracy depends heavily on the crew, as they have to prepare in advance the data they need. I think it could work as a start, but not very good for the long run. An ODAPI type device, or omni-directional ILS system (could be done, though much more complicated and costly) would be more useful.
Ambidextrous - Yes the glare might be bit of a problem, but not much. But it's all academics, if no one will take time to try and build a test system using today's technology.