That’s just a UBI with a different mechanism. The problem here is most proposals for negative income tax pay out annually rather than monthly (you specifically do not), and fail to account for people who do not work but otherwise provide useful input into the economy like stay at home parents and adults taking care of elderly family.
Because the people who need/would benefit aren't paying anything remotely near 1k/month in taxes, that's the whole point. Your solution only works in a society where people already have a reasonable amount of income.
either lower the tax or start offering monthly tax refunds?
would that work as an alternative or equivalent to UBI or am I thinking of something very different?