The more I think about this, the more I think that the most viable approach is to have it as a separate spin-off game, not as an expansion of Elite: Dangerous itself. Think for a moment about some of the combat scenarios, like boarding another ship (whether docked or in space) or sneaking on board to plant a tracking device, or steal something, or assassinate a passenger: the timescale of this kind of gameplay simply does not synchronise within the space and vehicle combat of Elite: Dangerous. It would be extremely challenging to devise FPS gameplay in which these activities can be resolved within the available timescale of a fight in spaceships or vehicles, to say nothing of the havoc that would be created by lag, instancing issues or lost connections. A FPS game (or third person, perhaps able to switch between the two) set in the Elite: Dangerous Universe has plenty of possibilities for gameplay but I don't see it as viable any more to add it on to Elite: Dangerous itself.
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The closest example I have personally played of combining space combat with personal/ground combat is Star Trek Online, where the two sections are not concurrent and you switch from one to another - you are not beaming aboard an opposing ship at the same time as controlling your ship in combat (there are boarding shuttles I remember that abstracted this activity but you just launched them from your ship at the cost of crew numbers, you were not yourself on board doing the fighting). Even this hybrid approach would face serious complications if integrated into Elite: Dangerous, like: what happens if you hyperspace with someone on board? Would you still be on board another player's ship if you logged off or lost a connection? What if they change ships? What if you infiltrate a ship in storage? There are so many problems like this, that having it as a completely separate game (maybe except for the background simulation) increasingly seems to me to be the only way around it.