Efficiency of solar panel under warm-white LED light
A transformer is the way to go.  Your claim of "Power is too low and voltage too high for a normal transformer to be viable" makes no sense.  Power being low is a good thing.  That means the transformer can be smaller, all else held equal.  High voltage does need to be considered, but this is done routinely.

Since this is a one-off and you're already looking at very low efficiency solutions, you can make this transformer yourself.  Get a long ferrite rod and wind magnet wire around a section at each end, leaving a long gap between the two coils.  That won't be very efficient, but will still be better than LEDs and a solar cell.

Figure air is good for about 1 kV per mm.  Derate that by half, so 500 V/mm for the gap between the two coils.  A 6 inch gap is good for 76 kV, for example.  I consider that "high" voltage.  Since you haven't given any other spec for voltage other than that it is "high", this meets your requirements.

Note that you can drive the transformer from much higher frequency than line voltage.  A few 100 kHz will help transfer more power across the same gap.  Or conversely, allow for smaller coils at each end.