In general, the solution is not to add a large existence term, but to make sure that the utility function as stated matches your actual preference for whether or not someone should exist.
What do you mean by "actual preference"? I can't think of many interpretations of that comment that don't implicitly define a utility function (making the statement tautological): even evaluating everything in terms of how well it matches our ethical intuitions constitutes a utility function, albeit one that'll almost certainly end up being inconsistent outside a fairly narrow domain.
Our intuitions evolved to make decisions about existing entities in a world dense with externalities. I'd expect them to choke on problems that don't deal with either one in a conventional way, and I don't trust intuition pumps that rely on those problems.
I do mean a utility function, but one not necessarily known to the agent. If one values all good lives but wants to consider average utilitarianism, they could make average utilitarianism less different from their real utility function by adding existence terms. However, if their real utility function says that a life should exist, ceteris paribus, if it meets a certain standard of value, regardless of the value of other lives, than they are not really an average utilitarian; average utilitarianism is incompatible with that statement.
Some people see never-existed people as moral agents, and claim that we can talk about their preferences. Generally this means their personal preference in existing versus non-existing. Formulations such "it is better for someone to have existed than not" reflect this way of thinking.
But if the preferences of never-existed are relevant, then their non-personal perferences are also relevant. Do they perfer a blue world or a pink one? Would they want us to change our political systems? Would they want us to not bring into existence some never-existent people they don't like?
It seems that those who are advocating bringing never-existent people into being in order to satisfy those people's preferences should be focusing their attention on their non-personal preferences instead. After all, we can only bring into being so many trillions of trillions of trillions; but there is no theoretical limit to the number of never-existent people whose non-personal preferences we can satisfy. Just get some reasonable measure across the preferences of never-existent people, and see if there's anything that sticks out from the mass.