Rebuilding my KR-2(kind of S)

I looked at the LED nav light problem myself after a guy posted his
lights for sale here. Neat stuff those LEDs and a good fit for many
lighting applications. Now to answer your questions:

3. In the Mouser catalog there is the Kingbright red LED part no.
L934SRCD rated at luminous intensity of 500 to 700 at an angle of 50
degrees.
How does this compare to the FAR 23.1391 minimum intensity of 40
candles?

At the peak (centerline), you'd need 80 (40/.5) LEDs to produce the
required intensity, but off center, you'd violate. The viewing angle
specs on LEDs often give anglr at which the intensity drops 50%. The
good news is that there has been a sort of breakthough in LED
efficiency in recent years, with outputs in the multi candle range,
not sure if you're going to get these from Mouser though. They are
more expensive, roughly proportional to their light output. So we're
talking a couple bucks each maybe.

Is the 50 degrees referred to in the Mouser catalog to be considered
conical?

Yes, although there are LEDs available that have different patterns in
azmuth and elevation.

As for powering your array, I wouldn't worry about a constant current
supply like the one guy did. Just stack them in series and put a
dropping resistor in series with each leg. Incandescent nav lights
fluctuate in intensity with the supply voltage and these will change
less then those.

Will overlapping these LED beams cause a violation of 23.1395 somehow?

IMHO, no. Just meet the min. intensity in the prescribed directions.

Regards