My comment above strongly called into question whether CDT gives the right answers. Therefore I wouldn't try to reinvent CDT with a different language. For instance, in the post I suggest that we should care about "all" the outcomes, not only the one happening in the future. I've first read about this idea in Paul Almond's paper on decision theory. An excerpt that might be of interest:

Suppose the universe is deterministic, so that the state of the universe at any time completely determines its state at some later time. Suppose at the present time, just before time tnow, you have a choice to make. There is a cup of coffee on a table in front of you and have to decide whether to drink it. Before you decide, let us consider the state of the universe at some time, tsooner, which is earlier than the present. The state of the universe at tsooner should have been one from which your later decision, whatever it is going to be, can be determined: If you eventually end up drinking the coffee at tnow, this should be implied by the universe at tsooner. Assume we do not know whether you are going to drink the coffee. We do not know whether the state of the universe at tsooner was one that led to you drinking the coffee. Suppose that there were a number of conceivable states of the universe at tsooner, each consistent with what you know in the present, which implied futures in which you drink the coffee at tnow. Let us call these states D1,D2,D3,…Dn. Suppose also that there were a number of conceivable states of the universe at tsooner, each consistent with what you know in the present, which implied futures in which you do not drink the coffee at tnow. Let us call these states N1,N2,N3,…Nn. Suppose that you just drunk the coffee at tnow. You would now know that the state of the universe at tsooner was one of the states D1,D2,D3,…Dn. Suppose now that you did not drink the coffee at tnow. You would now know that the state of the universe at tsooner was one of the states N1,N2,N3,…Nn. Consider now the situation in the present, just before tnow, when you are faced with deciding whether to drink the coffee. If you choose to drink the coffee then at tsooner the universe will have been in one of the states D1, D2, D3,…Dn and if you choose not to drink the coffee then at tsooner the universe will have been in one of the states N1,N2,N3,…Nn. From your perspective, your choice is determining the previous state of the universe, as if backward causality were operating. From your perspective, when you are faced with choosing whether or not to drink the coffee, you are able to choose whether you want to live in a universe which was in one of the states D1,D2,D3,…Dn or one of the states N1,N2,N3,…Nn in the past. Of course, there is no magical backward causality effect operating here: The reality is that it is your decision which is being determined by the earlier state of the universe. However, this does nothing to change how things appear from your perspective. Why is it that Newcomb’s paradox worries people so much, while the same issue arising with everyday decisions does not seem to cause the same concern? The main reason is probably that the issue is less obvious outside the scope of contrived situations like that in Newcomb’s paradox. With the example I have been discussing here, you get to choose the state of the universe in the past, but only in very general terms: You know that you can choose to live in a universe that, in the past, was in one of the states D1,D2,D3,…Dn, but you are not confronted with specific details about one of these states, such as knowing that the universe had a specific state in which some money was placed in a certain box (which is how the backward causality seems to operate in Newcomb’s paradox). It may make it seem more like an abstract, philosophical issue than a real problem. In reality, the lack of specific knowledge should not make us feel any better: In both situations you seem to be choosing the past as well as the future. You might say that you do not really get to choose the previous state of the universe, because it was in fact your decision that was determined by the previous state, but you could as well say the same about your decision to drink or not drink the coffee: You could say that whether you drink the coffee was determined by some earlier state of the universe, so you have only the appearance of a choice. When making choices we act as if we can decide, and this issue of the past being apparently dependent on our choices is no different from the normal consequences of our future being apparently dependent on our choices, even though our choices are themselves dependent on other things: We can act as if we choose it.