General ship skill. For example faster mining speed, faster response times e.t.c. Some large fraction of ship skill is from the captain, with the rest being from service crew. Full service crew skill requires filling the ship entirely with maximum skilled service crew. Marines count at empty slots as far as service crew skill goes, irrespective of the skills of the actual marine.
Nothing stops you having 5 star marines which are also 5 star service crew. Morale is used in both rolls and you can level up engineering and boarding by changing the role of the crew person. Such crew could also be 5 star managers and 5 star captains if they were levelled as such.
Most realistic/sensible option would be that the ship gets an order to fly to an equipment dock and orders on more crew. The crew that gets placed is special and matches the roll profile of the ship job, similar to when the ship is built. This would mean that players need to repeatedly board the ship in the same location and not leave it alone for any length of time.
In addition to this the AI should respond to being boarded and send a large defence fleet to guard the ship. These ships should defend the boarded ship when near and become hostile to anything it is hostile with. The ships should then guard it until it can make its way to an equipment dock to replenish its crew. This large defence fleet should instantly hostile the ship if boarding was successful and attempt to destroy it for 30 to 60 minutes.
The player already has a lot of options to replenish crew and move crew around from the map view. No walking on platforms required, unless you want to find reasonably skilled crew.