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This would depend on how those pieces are defined. If they are treated as making two separate moves on the same turn, and the second move is capable of checking the King, things could prove difficult.

Moves in general are a succession of 'legs', each leg having a specified step, but possibly undetermined length (for rider legs). The move generator treats the legs in the order they occur in the move: first it tries to realize the first leg, (i.e. find destinations for it that are compatible with the 'mode' of the leg, e.g. contain an enemy piece if the leg must capture) looping through all possible realizations, and for each of those recursively calling itself to treat any remaining legs. (And when it realizes the final leg, deliver the move). I suppose this is very much like what you call 'making separate moves in the same turn'.

I wonder if it makes sense to try saving on doing a full move generation for the opponent (in the position before the move). Because that move generation is also used to mark all the attacked squares, so that it is known which moves of the royal stumble into check. So it is not only a matter of deciding whether the royal is under attack, but also whether all squares where the royal can go are under attack. Without that information, you would have to test each move of the royal separately. In the case of an orthodox King that would be 8 moves, so even when you safe a factor 8 on the test because you have to try only a single move for each piece, you sitll have no gain over doing all moves of each piece once. And what exactly you would have to do would depend on how the royal moves, which makes it hard to use tricks to speed it up.

So I guess for now I stick to generation of all (pseudeo-legal) moves for the side to move (to create the list needed for highlighting), and, in the same position, a full move generation for the opponent. During which attacked squares are marked, and when these contain an enemy piece and an attacking slide has not yet exhausted its range, tabulate the origin and move of that attack with the square. So they can be retried in reply to moves that moved that piece away (to test whether it was pinned), or after every move when the piece was royal (to see if the pre-existing check was resolved).In most positions you will not be in check, and most pieces will not be pinned, so the common case is that nothing has to be done on a per-move basis. Only if the game contains 'unpredictable' pieces, such as hoppers or hook movers, then you would have to generate all moves of those in reply to every move of your own.