the inflationary pressure of just adding $x to everyone's income.
Like the cities that are implementing $15/hr minimum wage, it wouldn't be a sudden $x. (I should mention that this is all with an 'ideal' and thought out plan) You'd have a year of $1 just to make sure all systems are set up, then a year of $x/100, then $x/10, then $x/2, then $x. (Or an even more gradual roll out.) During this time wages would likely stagnate across the board, but income would increase. Min wage probably decreases in the same fashion until it's $0, rather than just being completely and instantly removed. Then $x is pegged to inflation.
With a gradual roll-out the year-over-year inflation should not be much larger than it would otherwise have been (disclaimer: I am not an economics shaman).
The other problem I don't know how you deal with is what prevents a UBI from simply raising the price of everything by the amount of UBI everyone gets? How do you guarantee food, shelter and clothing will be always available at UBI income rates without price controls?
While income increases, wages will depress, so at the end most people will see a financial wash except for the very bottom rung, who now has income, and the very top rung, who probably have higher taxes. After that, what "free market" forces actually exist are still in place. If property companies try to raise their rents by $x, they'll find a lot of tenants leaving (especially now that they are able to better move around the country, and aren't locked to a city). Similar things will happen for food and clothing: companies that try to super-hike will be undercut by those who just go with inflation.
A minimum wage hike doesn't lead to large inflation, and mincome is essentially a replacement for such a hike while also increasing the pool of people who have money to spend.
As for guaranteeing, that's where the government decides what $x is, based on the cost of basic housing, food, etc. This is one reason it might make more sense to have a per-state $x (and you deal with people changing states in much the same way you deal with immigration, except that after they move they would receive the amount from their prior state until they've been settled for Y months). Could companies hike to match $x? Maybe. What's stopping them from maxing out those prices right now, though?