The problem isn't money, per se. As others have noted, money is a very effective mechanism for exchanging labor and goods. The real problem with capitalism is the flows of money. As you observe, there is a mismatch between what a capitalist society spends its money on, and what the citizens of that society believes are important. For instance, everyone thinks that teachers are important, but nobody wants to pay more taxes to increase teacher pay. Many people likely believe that social workers are helpful members of society, but nobody wants to pay higher taxes to pay them more than minimum wage.
The first problem is: where does money come from? You mention UBI, which is the first step in the right direction. Traditionally, UBI would be funded via tax revenues. You mention a wealth tax, and so I presume that your society would fund UBI via taxes as well. Capitalism creates money during the loan origination process (central banks also create money, but broad money is the bulk of money in a society, and this comes from private banks). And thus, bankers decide what economic activity is valuable and should be funded. On top of that, investors further decide what is important. And how is that working for us?
Well, we have widespread poverty, massive inequality, weak infrastructure and social services, etc. So perhaps the difference between modern capitalism and your utopia is that capital is not deployed efficiently. And yet, that is clearly not true. Capital is deployed efficiently, which is why we have trillion dollar corporations. We have filthy stinking rich companies and people. Capitalism clearly works. It just doesn't work for everyone.
What if you took the money creation function away from bankers and investors and put it in the hands of the public at large? The problem with bankers is that they need to turn a profit. And investors are just looking to line their pockets. The capitalist assumption is that these incentives will lead to optimal social outcomes, but the reality is far from it. Instead of funding services via taxes, what if you simply created the money for them out of thin air? Then, you just need to decide how and when to do so.
What if public services were funded by public contracts which are proposed and voted on democratically? The way the funding could be adjusted is that each service is also rated by the public on the quality of delivery, efficiency, etc. Sectors with low ratings would get increased funding, and sectors with high ratings would have stabilized funding.
Of course, you can't just print money forever. You will inflate your economy out of existence. Most people will say you just can't print money as I've suggested above at all. It won't work. But that's not true. You just need to destroy money as quickly as you create it (on average). You mention communal ownership of property, and this is a convenient place to send money back into the aether. Nobody can "own" land; they only rent it. But if nobody owns it, who does the rent go to? Well, it goes into the aether! In this way, the total rents across society can balance the rate of money creation via public goods and services. If inflation starts to take hold, just raise rents across the board. If deflation becomes a risk, then lower rents.
Framed this way, it is easy to see that rents are a kind of hidden tax. And yet, they are a tax that most people would be happy to pay, because they are already used to paying rent. And, clearly, land and buildings are an exclusive resource that can only be used by a few people at a time. There must be a deconfliction strategy for land use, and rents are a perfectly good mechanism.
But how to set the rent, if nobody actually owns the land? Well, just let potential renters bid on lots via auction. The market can set the price. Then, when money destruction needs to increase, then all rents go up by some proportion, on top of the contractual winning bid (or, if necessary, they increase progressively). Renters are definitely exposed to rent increase risk, but presumably they can recover it by raising prices, which causes more money to flow into the burn pit.
This system works better for the simple reason that it distributes economic power across all of society, rather than concentrating it in the hands of the financial sector. Society can literally choose to spend money on anything it deems to be "socially valuable" or "pro-social", regardless of its profit potential. Of course, people who have amassed wealth are still free to start businesses with their own capital. But if someone wants to start an organization whose purpose is not to make money, but to do good, then society can support and perpetuate that organization simply by designating money to that cause. Such grants can be time-limited (like 1-2 year funding at a time) so that when the organization fails to live up to its charter, the public can shut them down unceremoniously.
This kind of system allows each person to achieve their potential by following their passions, so long as their passion aligns with the rest of society either by: 1. producing a product/service that customers want to buy, at a profit, or 2. producing a product/service that a majority of citizens believe is worthy to be funded via a public grant. Since this system allows the same kinds of corporations which capitalism produces, it should produce an economy/society with strictly greater degrees of freedom than capitalism. It also allows people to succeed by chasing virtue rather than mere profit, while not condemning profit to a moral backwater.