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Just to act as devil's advocae: The main drive for developing shuffle
games is to make development of opening theory much harder, by presenting
the players with an unpredictable array. The price of someimes getting an
unplayable, and always a les aestethically pleasing setup is taken for
granted. But having them decide about which swaps to make kind of subverts
this purpose.

If I uderstand your prescription correctly, one can make 5 x 5 = 25
shuffles this way. (Each side can swap the center piece they have to swap
for 5 others: everything except Rooks and the Bishop of the other color.

Note that ICC supports several shuffle variants: except FRC there is
wildcastle (K&R stay in place), nocastle (shuffle all, but symmetric
setup), random compositions (but only one King each, and symmetric), or
independent random shuffles of everything for white and black. Unlike FRC
they are basically all just normal Chess with a different initial position,
and there are more 'wild' variants like that, which do not satisfy the
criteria one uually puts on opening arrays. (e.g. all Panws starting at
4th/5th rank, or white starting at 7th/8th rank and black at 1st/2nd). 

In winBoard I added an option to play every supported variant as a shuffle
game; how it exactly shuffles depends on the existence and type of castling
rights. I did not implement asymmetric shuffles yet, though; perhaps I
shuld offer that too.