I've mulled that idea over also... maybe have a 'safe' reinc option that's
just like the reinc system now.. and then other types of reincs that introduce
varying degrees of randomness.
I.E.
Mild could be like you mentioned. Normal, but the stats would be +/- some
random amount, but have all the +s and the -s total to zero
Moderate could be something similar but more variable.. or maybe just random
background

Unsafe could be random background, random race (maybe limit it to
recommended/suggested columns), plus soul freeze for a month

There's a lot of things you could do without screwing the whole system... In
fact, if you keep the 'safe'(current) option, there'd be no reason for anyone
to complain.

(though i'm sure someone would find a reason)