But without infinity, a system cannot examine itself, only subsets of itself. Even for the two copies in lockstep, you need a system at least two times as big as the one being examined.
I disagree, look at quines. Systems can contain copies of themselves if they can be compressed.
A quine prints a copy of itself, it does not contain a copy of itself. The copy contained in the quine is not executable in its compressed form.
There is a general theorem that says that for any computation, you can write a program that executes that computation on its own source code. The quine is only a special case.
Two is much smaller than infinity.
But the 2x systems still cannot examine itself, but only half of it (being optimistic, because in addition to the 2x you also need the logic doing the stepping and the comparison). There is no finite system that is a true subset of itself.