I would stop worrying about ranking so much. Rankings are not the full story. You need to do substantially more research into a department than just looking at its ranking.
What kind of hep-th are you interested in? For example OSU has Samir Mathur who is very well known in the quantum gravity...
In theory (i.e. not numerical) I would say higher order self-force corrections, formulations of extended body motion, two-timescale and post-Newtonian calculations of binary inspirals, modified theories of gravity, higher dimensional GR, stability problems for black holes (including things like...
Classical gravity is certainly a mainstream field, albeit a small one. The only schools in the US I know off the top of my head that have dedicated GR research groups are Caltech, UChicago, and Cornell. LQG on the other hand I would say is not mainstream in the sense that it has a competing...
When you say HEP theory do you mean particle phenomenology? Or are you talking about research areas more akin to those you'd see in HEPT on arxiv i.e. string theory, field theory, semi-classical gravity?
Also, while Penn State is certainly good for HEPT, Ashtekar mainly does classical gravity...
Yes. I know several people who have.
At the undergrad level the point is to learn how theory research works. Publishing a paper is a bonus.
This isn't true. I'm currently doing undergrad research in two theory groups: a classical GR group and a quantum gravity group. I've been doing research...
Well then that should be your top priority, especially if you want to do theory in grad school. Furthermore if you get an idea of what theory research is like then your question will start to answer itself through practice. Meticulously working through every page of a textbook will be a complete...
I meant have you had any experience working in a theory research group? I ask because what you mentioned in your OP seems to be an attempt at addressing the question of "what makes a successful undergrad physics major" not "what makes a successful theorist". Nothing you mentioned really has much...
If you don't show any of your work, how are we supposed to help? We don't know where exactly you got stuck. For example, did you make sure to work to only first order in the perturbation when computing the connection coefficients?