I see your point.
Maybe a solution would be not to have an increase on income tax. We could have some kind of tax on capital, carbon tax, or any tax that isn't linked directly to a salary to finance the basic income.
The falling labor participation for me is one the reasons to implement a basic income. Because I think new technology will soon be burning more jobs than creating jobs. Which is not a bad thing for the economy in general, but is a bad thing for redistribution of wealth. So in that sense it would seem fair to find the money at companies (or people who own companies) that are creating a relatively small amount of jobs.