This is an interesting idea. One thing someone could do is make a machine which takes some enumeration of all Turing machines and runs the mth machine on the input of the last k rounds with them inputed in some obvious way (say 4 symbols for each possible result of what happened the previous round).

But a lot of these machines will run into computational issues. So if one is using the run-out-of-time then automatically defect rule most will get killed off quickly. On the other hand if one is simply not counting rounds where a bot runs out of time then this isn't as much of an issue. In the first case you might be able to make it slightly different so that instead of representing the mth Turing machine on round m, have every odd value of m play just Tit-for-Tat and have the even values of m simulate the mth Turing machine. This way, since tit for tat will do well in general, this will help keep a steady supply of machines that will investigate all search space in the limiting case.