Woops, quite an embarassing mistake I made there! Another minor mistake was that I said you had to use 36, 37 etc.. in fact they're 5 times the same number. Because the number of cards decreases with the number out suits.

But yeah, the position thing is true though What you said about mathematical equivalence, that only counts for when you switch the suited cards amongst themselves; Switching an unsuited with a suited is a mathematically different situation.