Against per se ordered infinite sequences of causes

Say that a sequence of events is per se causally ordered provided that each event not only causes the next but also causes everything in the next that is involved in causing the one after that (if there is one after that).

1. Any possible chunk of contingent reality is such that it is possible for something internally just like it to have a cause.
2. It is not possible to have a cause for an infinite per se causal regress of contingent causes.
3. Anything internally just like an infinite per se causal regress of contingent causes is an infinite per se causal regress of contingent causes.
4. So an infinite per se causal regress of contingent causes is impossible.

In the argument, (1) is a weak causal principle. The reason for the "something internally just like" phrase is that without the phrase the premise would immediately imply that every possible chunk of contingent reality has a cause given essentiality of origins. Premise (3) requires a non-Humean account of causation. I am going to ignore metaphysical questions about chunks of reality: perhaps we can reformulate in terms of pluralities, perhaps in terms of sets.

A crucial controversial premise is (2). Here's an intuitive line of thought that inclines me to (2). Suppose we have a backwards-infinite per se causal sequence of chickens and eggs, each chicken fully deterministically causing an egg with all of its relevant causal power, and each egg deterministically causing a chicken with all of its relevant causal power. And imagine this regress has a cause, say, G. How can G cause that whole sequence? Well, it couldn't do it by causing one particular chicken or one particular egg, for that wouldn't account for the chickens and eggs that came before that. The only picture I get of how something could cause the whole sequence would be if it caused each one of the eggs and chickens, or each one prior to some point in time, or more generally some backwards-infinite subsequence. The argument will be the same in each of the three cases, so I will just focus on the simplest.

So the cause G caused each of the eggs and chickens, and thereby caused the sequence. But of course each egg is caused by a chicken, too. So a given egg has two causes: it is caused by a chicken and by G. But the chicken caused the egg fully, with everything the egg needed to do its job of causing the next thing. So what did G contribute? Nothing really crucial to the sequence, since everything crucial to it was contributed by the chicken. Rather, it looks like it's going to be a case of overdetermination. The egg is caused by G and it's caused by the chicken. But G's causing of the regress as a whole isn't overdetermined (or so we may surely assume, modulo some technicalities), since in the absence of G the whole sequence wouldn't be caused. And if you take away a non-overdetermining cause, the effect disappears. So if you took away G, the whole regress should disappear. But why should taking away G matter, given that all of the causal influences by which G allegedly causes the regress are individually overdetermined?

If this is all right, then the critical attention will shift to (1).