I don't think I need 624 sequential values, if I know I'm on second roll and I know the algorithm behind the initialisationI don't think you are going to have a whole lot of luck with trying to work Mersenne backwards as you need 624 sequential values to even predict future iterates (you can also likely use them to figure out past, back to seed, too).
t[0] = Initial SEED
t[n] = (( upper 2bits of t [n-1] ) xor t [n-1]) * 0x6c078965 + n
where n = 1 - 623
(taken from page 21).
I need to check into Mersenne, again - but if I recall correctly, only two or three of these previous values are taken. With second roll, these should be rather fixed.
Still I'm not sure whether this rollback would be possible - if second mersenne roll is not bijective, then we'd be stuck with anyway.
TCC