Okay, neat! I have an idea, and it might be kind of farfetched, or not amenable to the types of analyses you are best at doing, but I'll share it anyways. Here goes.

Given that there is a tradeoff between health and reproduction, I wonder if you could increase the expected lifespan of a healthy human male by having him take anti-androgens on a regular basis.

We already know that male eunuchs who are humans live longer than intact male humans. I suspect that most guys wouldn't be willing to become eunuchs even if they valued having a long lifespan very highly, but being able to increase one's expected lifespan by decreasing one's testosterone levels while still remaining intact might be something that a few males would consider, if such a therapy were proven to be effective.

Anyways, after taking 10 minutes to look around on Google Scholar, I wasn't able to find any papers suggesting that taking anti-androgens would be an effective anti-aging measure, so maybe this would be a viable project for someone to work on.

As an aside, I don't know which mechanisms cause castrated men to live longer, but this seems relevant to the question of why/how castrated men live longer.

To answer your questions:

• SENS has a page that might help answer the first question you posed above.
• You could email Audbrey de Grey and ask for ideas. (The page I have linked above seems to suggest that he is highly open to receiving emails from intelligent people who are interested in doing anti-aging research, so don't let the fact that he's internet-famous prevent you from sending him a note).
• In response to 2, I would say that it seems like you are already highly skilled, such that you could dive in and tackle any problem(s) you decide to start working on immediately. People gain skills by working on hard problems, so it doesn't seem necessary for you to take additional time to explicitly hone your skill set before starting on any project(s) that you want to work on.

To answer your questions:

• SENS has a page that might help answer the first question you posed above.
• You could email Audbrey de Grey and ask for ideas. (The page I have linked above seems to suggest that he is highly open to receiving emails from intelligent people who are interested in doing anti-aging research, so don't let the fact that he's internet-famous prevent you from sending him a note).
• In response to 2, I would say that it seems like you are already highly skilled, such that you could dive in and tackle any problem(s) you decide to start working on immediately. People gain skills by working on hard problems, so it doesn't seem necessary for you to take additional time to explicitly hone your skill set before starting on any project(s) that you want to work on.

Examine people who do intermittent fasting to promote autophagy.

I should clarify something: the types of problems I can most efficiently tackle are retrospective analysis of already-collected data.

Prospective clinical and animal studies are not out of the question, but given the investment in infrastructure and regulatory compliance they would need, these would have to be collaborations with researchers already pursuing such studies. This is on the table, but does not leverage the clinical data I already have (unless, in the case of clinical researchers, they are already at my institution or an affiliated one).

My idea at the moment is to fit a hidden Markov model and derive a state model for human aging. But this pile of clinical data I have has got to be useful for all kinds of other aging-related questions...

I also find that line a bit strange. In nearly all cases where I would expect that someone says: "I'm beginning to find this conversation aversive, and I'm not sure why" I think I would take it as a topic change to why the conversation might bring up negative emotions in the person.

If we are in an environment of open conversation and I say something that brings up an emotional trauma in another person and that person doesn't have the self-awareness to know why he's feeling unwell, that's not a good time to leave him alone.

The tough part will be guarding against Goodhart's Law. I suspect that the current system of publications and grant money as an indicator of ability started out as an attempt to improve the efficiency of scientific progress and has by now been thoroughly Goodharted.

As Lumifer points out, tenure was intended to give productive scientists some protected time so they could think. However, the amount of hoops you jump through on the way to getting there puts you through the opposite of protected time so by the time you get tenure you've gotten jaded, cynical, and acquired some habits useful for academic survival but harmful to academic excellence.

I can offer advice on statistical analysis of data (frequentist, alas, still learning Bayesian methods myself so not ready to advise on that). Unfortunately, right now I have too little spare time to actually analyze it for you, but I can explain to you how you can tackle it using open source tools and try to point you toward further reading focused on the specific problem you're trying to solve. In the medium-future I hope to have my online data analysis app stable enough to post here, but this is not looking like the month when it will happen.

I can probably answer almost any question you have about the R language, many questions about the Shiny framework, and some questions about Javascript, PHP, and various flavors of SQL (though there are probably plenty LW-ers more knowledgeable than I on the latter three topics).

Also can advise on designing controlled animal experiments so that you won't regret painting yourself into a corner later, but I'm guessing there aren't many biologists here.

I apologize in advance for slow turnaround times. My schedule is pretty full of kids and work. :-/

PS: if your question is too lengthy to post here, just post it on the appropriate Stackexchange site and post the link here.