"What is the best way?" is a very difficult question to answer. What are your objectives? Are you running into performance problems? Do you want to generalize? I really don't think there's any way to answer your question without a lot of guesswork.

As for feedback on your Mathematica code, I think your SolveInnerLoop function could be simplified to this:

SolveInnerLoop[S_, \[CapitalGamma]m_, \[Beta]_] :=
 Sum[Log[astar[s[[1, n, 1]], \[Beta], s[[1, n, 2]], \[CapitalGamma]m]], {n, 10}]

Well, all I can suggest is that you find a way to ask your question more concretely. There's just no way for me to guess what could be going wrong. I'd need to see what you're trying to do. I'm honestly not even sure how to interpret your question. By "a more complex inner loop" do you mean a different version of SolveInnerLoop, or is there something else that you haven't shown us yet?

Are you thinking that there's some general strategy that we can just tell you that you can then apply that somehow avoids whatever difficulties you're having? If that's what you're asking for, it seems to me that you're on the right track--I can't think of some general strategy that's always superior to what you're doing. But again, if I knew more about your real context, maybe I could identify some particular opportunity.