Check out the common TV masthead amplifier setups to get some clues how to send power up the coax like you want to do. Inductor and capacitor needed at both ends to pass the DC and vhf (AC) signal respectfully.
This is a solution that reduces cabling aloft and easily achieved. The two electronic components reqd at the top are so small that is just as easy to totally encapsulate in sealant
for moisture protection which is essential for the coax anyway.
Excellent suggestion from Paul re polarity change between anchor
and sail mode lights -all thats needed at the top are two extra diodes -actually only one extra if you utilize one of the LED's as one of the polarity diode.
Have you thought of changing to non mast
installed nav lights? Only difficulty is with the steaming light which needs to be 2.5m above the side lights but this is easier to do on the mast at a lower height perhaps combined with spreader light. For the vhf, being line of sight, height obviously does help but practically speaking I'm not so convinced that the extra range is worthwhile to have the antenna
go all the way to the top. I'm currently using a J pole vhf antenna mounted off the arch and have no wires up to the top. If I wanted the extra hight this is what I'd do: Mount the antenna on a " travelling car" that slides up the backstay using cable ties for the coax. Hauled up with the main halyard
with a "ring" around the stay and a temporary 'downhaul' rope
and retained at the top similar to a halyard
lock fitting. To bring down (for replacing the cable ties that would not last) simply run up the halyard and ring up to release the halyard lock. No dedicated halyard necessary and easy to maintain without climbing the mast.