If you want to keep thinking about the “there can’t be a single number objection”, I recommend looking at what philosophers have said about supervaluationist solutions to the sorites paradox. On some supervaluationist views, its possible for claims like “there is a single exact level of hedonic level of well-being you have right now” to be true, even though there is no sentence of the form “[n] is your current level of well-being” that is true. Sounds contradictory, but in fact, it is merely strange, not a formal contradiction, and reasonably well-motivated by the need to solve the sorites paradox itself. Supervaluationism can be deployed whenever there is some reason to think that something lies somewhere on a scale, but also it seems absurd/silly to think that there’s an exact point on the scale that is the place where it lies exactly. So people who think that there is a single well-being scale that can be captured with real numbers, can try and block your argument against this by claiming that supervaluationism can account for the sense in which it is wrong or misleading to say that you have a precise level of well-being right now, without giving up the idea that well-being can be represented by a real-number scale. Not that supervalutionism is obviously right, or uncontroversial or anything, but it’s an obvious thing for people to try here.
If you want to keep thinking about the “there can’t be a single number objection”, I recommend looking at what philosophers have said about supervaluationist solutions to the sorites paradox. On some supervaluationist views, its possible for claims like “there is a single exact level of hedonic level of well-being you have right now” to be true, even though there is no sentence of the form “[n] is your current level of well-being” that is true. Sounds contradictory, but in fact, it is merely strange, not a formal contradiction, and reasonably well-motivated by the need to solve the sorites paradox itself. Supervaluationism can be deployed whenever there is some reason to think that something lies somewhere on a scale, but also it seems absurd/silly to think that there’s an exact point on the scale that is the place where it lies exactly. So people who think that there is a single well-being scale that can be captured with real numbers, can try and block your argument against this by claiming that supervaluationism can account for the sense in which it is wrong or misleading to say that you have a precise level of well-being right now, without giving up the idea that well-being can be represented by a real-number scale. Not that supervalutionism is obviously right, or uncontroversial or anything, but it’s an obvious thing for people to try here.
This is a good introduction to the sorites and supervaluationism: https://plato.stanford.edu/entries/sorites-paradox/