I wouldn't want to clean public toilets if I didn't need to do so. You'd be willing to do it for free. I think one of our views runs rather closer to the overwhelming majority of people, like 99.999%, than the other. This issue is really not the one you want to argue. But I understand that you have to argue it, because if you simply accepted this point then you must accept the fundamental problem. When everybody starts demanding substantial amounts of money for any labor they don't want to do, you're not only going to crash your gdp but see hyperinflation as well.
Now not only is the basic income pointless because it's no longer enough to afford anything (and increasing it further just sends you closer to Zimbabwe), but you'd also completely crash your currency meaning you'd also no longer be able to afford any imports (though exporters would be getting filthy rich - see: why China intentionally devalues their own currency). The country would be obligated to rapidly transition, formally or informally, to another currency as the default unit of trade for anything of value, further nullifying the basic income.
You're getting way too strung up on the specific example of cleaning toilets. You know what job vastly more people will want to do? Installing and maintaining a self-cleaning toilet. Bang, massive benefit to the local community. Focus on profitability creates a blind spot.
I don't see why you think inflation would suddenly happen. You haven't justified that claim.
It doesn't matter whether the overwhelming majority of people would be willing to clean toilets for however much money: what matters is whether enough people would that the toilets get cleaned. From what I can tell, the answer to that is "yes".
Given instructions, and absent other immediate obligations, I would do so much helping out, wherever I happened to be at the time. (The only reason I don't now is because I don't understand most jobs – my meddling could do more harm than good –, and they won't let me do jobs in my area of expertise.) I'm not unusual in this regard: perhaps I'm unusual in that I'll do this unprompted, but if it's a societal expectation that people clean up after themselves, and leave things in a slightly better state than they found them, people generally do it.
The problem is not a lack of workers. The problem is not a lack of things that need doing. The problem is a lack of "jobs". UBI (with the necessary patches to, e.g., prevent bad actors from redirecting all the money) is essentially employing everybody to do what they believe needs doing.
So the question becomes: do you believe direct democracy works at small scales? Your answer appears to be "no".