There's no reason why NIT needs to involve large amounts of paperwork. NIT only involves income, so a person simply needs to give their income (unlike taxes, which are much more complicated).
The NIT would presumably have a minimum amount given even if you earn 0$. That amount can be given to everybody can't do the paperwork. Then, the amount remaining above that can be distributed as a NIT.
Basically, give UBI to people who can't do the paperwork to cover them. The rest can use NIT.
The time lag is not a necessary property of the tax system. The NIT can be done on a monthly basis.
Anyways, this is just an implementation issue. Either way they both redistribute money.