I converted all bulbs on hull № 350 to LED in 2013. I faced the same problem as you have.
For my overhead lights, the two-pin socket which comes from the Amel factory aligning vertically consists of a brown or black bakelite terminal with the electric wires coming in the back and the two pins exposed to the center of the light assembly.
This bakelite terminal is held in place by a little screw. The bakelite terminal is elongated in such a way that when the little screw tightens, it automatically rotates the pins to the factory vertical position; i.e., if you loosen the screw, rotate the bakelite terminal 90°, and try to tighten the screw, it will inevitably rotate the bakelite terminal back to the Amel factory position with the pins aligned vertically.
In 2013, no suitable LED existed with vertically aligned pins, much less in the warm light variety we required, and which proved very hard to find.
So I took an abrasive tip on a dremel, loosened the screw, pulled bakelite terminal so I had one or two inches of electric wire exposed (for ease of work), and wore down the Amel factory elongation on each bakelite terminal. Sometimes upon retightening the screw the base still rotated a bit so the LED was not perfectly horizontal, but frankly, this does not impact light distribution in any perceptible way. One or two of mine are crooked enough that one edge of the flat disk LED may be touching the diffuser glass, but I don't think anyone has ever noticed.
It takes a bit of time. And I ruined one of the LEDs in the process of installing, but so far, only one LED has burned out, just a week or two ago.
SM2000 № 350 (2002)
Underway, Thermopylae to Sciathus