The attempt needs more accurate figures where you write "completely", because 99%, 99.99% and 99.9999% are not the same effort.
And for instance, is at least the heavy water more pure than the sought sulphuric acid?
I wonder - maybe a silly interrogation, but: can H20, H3O+, SO42-, HSO4- swap their oxygen atoms? If this happens, even at a slow pace, then 18O won't stay pure in the water, as some 16O will leak from the SO42- part. This gag happens with 2H.
For the sought solution, several steps may be necessary, depending on the desired 18O purity and the achievable dehydration. Like:
100% 16O, dehydrate as possible, add 18O to obtain 90% 18O,
again dehydrate as possible, add 18O to obtain 99% 18O,
again and again
During production and storage, air moisture may be a difficulty.