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To get back to Spartan Chess:

I doubt if shuffling the initial setup can create enough difference. I
agree that the proposed array seems the best, but as all pieces can jump
over the Pawns it is not terribly critical where you put them. The rule of
thumb is that 3 tempi is a Pawn, and we need to bridge more than a Pawn.
Even if you would make the Lieutenants and Colonels obstruct each other by
having them jump to the same square, that would only take 2 moves to
correct. (And a second move with the same piece to evacuate the square for the other might even be partly useful.)

Similarly, the sideway Lieutenant move is not worth very much. I tested the value of such moves on Bishops once, and there was almost no benefit compared to a plain Bishop, (about 0.25), as long as these came in pairs. The double Hoplite push will be worth something, but as the Spartans are not really dependent on Pawn moves for their development, I doubt it will be much. (It would be interesting to test it, though.)

Having artificial rules like the pinning of Hoplites is something I
generally dislike. Let me suggest two more options for trimming the Spartan
strength:

1) reduce the value of the General or Warlord, by using the corresponding
crowned slider rather than the knighted one. I am currently running games
whwer I replaced B+N by B+K, which should be worth R+0.25. The Persians are
leading there 24-18 (so not yet significant, but quite a change from what
it was). If this is too much, the R+N could be replaced by R+K, which
should be around 7.

I think the main problem is that the Hoplites are better in the end-game
than FIDE Pawns, so that the Persians need stronger piece material to hold
them back. Normally, trying to balance a significant Pawn advantage with
pieces unbalances a game, because in the middle-game the Pawns are
irrelevant, and the stronger pieces lead to quick checkmates. You can
always balance the over-all result to 50%, but you will get a game where
one side must inflict a quick middle-game checkmate, or he will be doomed
with certainty in the end-game. This is usually not very interesting. In
Spartan Chess, however, a quick middle-game mate is not easy because of the
dual King. So we can afford much larger strength differences in piece
material than usual without running into this problem.

This brings me to the second proposal:

2) If the problem is that Hoplites promote much easier than FIDE Pawns in
the end-game, it might be possible to offset this by strongly reducing the
value of the piece they promote to. So much, that a single promotion is no
longer decisive, but you need two. (Assuming that it is about as difficult
to promote two Hoplites as it is to promote a single FIDE Pawn.) So perhaps
it would work if the Hoplites are forbidden to promote to G or W. The
preferred choice than probably would be C (which has mating potential).
This would also provide more incentive to promote to K, which might be
stronger than C, but is so much weaker than G or W that the possibility to
promote to K in Spartan Chess in the current rules is of as much practical
relevance as promotion to B in orthodox Chess (namely none...).