Spartan Chess

I learned about this variant today and think it's super cool! I played a couple games on Pychess. I think you might be able to make a decent version of it on Chess.com's variant editor, but I'm not sure if the two king set up would work.

What you refer to as 'half-royal' (or 'third-royal' etc.) is more commonly known as 'extinction royalty': you would only lose when all your royals are captured, or, in case a checking rule applies, you would be checkmated when you cannot move your last royal to safety. This in contrast with 'absolute royalty', where you already lose when one of your royal pieces gets captured, or cannot be saved.

The duple check rule is a kind of intermediate. It can be generalized to more than two royals as the requirement that after your move at least one of your royals should not be under attack. And this allows for an entire spectrum of such rules, where with N royals at least M should be left not under attack. When M=N this gives you absolute royalty.

As to en-passant. In Spartan Chess Hoplits obviously would never be able to capture a Persian (FIDE) Pawn, as they would only attack the square the latter moved through from the square that is now occupied. The Persian Pawn can attack a square a Hoplit jumped over, e.g. after He7-c5 it would attack d6 from e5. But it would be very illogical to then allow capture of that Hoplit on d6. Because it was a square that was not visited at all by that Hoplit. Unlike Persian Pawn double pushes, which cannot jump, the Hoplit initial move is a jump.

Allowing e.p. capture on a square the piece jumped over opens a can of worms, as, as you mentioned, that square could be occupied by an enemy, and would raise the issue of double capture. Inconsistent rules often create such problems. In addition I could add that complex special rules are usually a bad feature in any variant, deteriorating its elegance, and thus should only be specified when the problem they solve was even worse. In orthodox Chess the e.p. rule was a necessity to prevent the double push (which in itself was a very desirable feature for curing boring opening play) from breaking the passer situation: without double push Pawns would be prevented from reaching their promotion square by any enemy Pawn in the adjacent file that is on a rank before it. Hoplits and Persian Pawns can in general bypass each other anyway, and giving the Hoplits an initial jumping move cannot spoil anything. So there is no need for e.p. capture here, it would just be complex rule added for the sake of cmplexity, where the goal should be to strive for simplicity and elegance.

As you already discovered the R+N compound, being about two Pawns stronger than R+K, would give the Spartans an overwhelmig advantage. Taking away the jump of the Spartan Captain and Lieuteneant would make these pieces a lot weaker, and spoil the balance in the opposit way. Besides, it would make them just crippled versions of Rook and Bishop, rather than adding something new and invigorating to the game in the form of the orthogonal or diagonal jump.

The Spartan army does not really need castling. In orthodox Chess castling was added to solve the problem that you cannot bring your King to a safer fortress without trapping your own Rook, and you have to irreversible break your Pawn Shield to let the two pass each other through ordinary moves. But since most Spartan pieces can jump, they would not be trapped when you move a King towards the corner with an intact (Hoplit) Pawn shield. In addition, King safety isn't all that important for the Spartan army, as it has a spare King. And Hoplits do not nearly make such a good fortress as Persian Pawns anyway; they could only protect each other by opening files. So the Spartans have to device other methods to keep their King safe rather than putting it near the corner behind a closed rank of Pawns. That makes Spartan castling another complex rule for the sake of complexity.