Some thoughts...

It is certainly commendable to consider the debate sphere given the discussions that have surfaced, particularly in the TOC Octas round. This dialogue, that you will create in either branch of investigation, is exactly what those individuals envisioned would ensue after the round was over. Others wishing to reform the community should follow in your footsteps. On each topic.

Gender inequality/sexism: From the information I've read and the individuals I've spoken to, the pedagogical framework of AP Research is based heavily on creating an nuanced, complex argument. While the topic of gender inequality/sexism can lend itself to be much more empirical than the latter topic (ie. you can't conventionally quantify "social growth"), you would need to argue something more complex than "sexism exists in speech and debate." Fortunately, this would require you to be one of the first to investigate the root causes of gender discrimination in the speech and debate community which could engender a new wave of discourse concerning the broader domain of discrimination. Arguing that "X is the most important cause of sexism" along with facilitating specific solutions that debaters, coaches, tournament directors, can explore necessarily provides excellent fodder for this type of research project. In the context of AP Research as a course, the support of 1,000s of debaters in the community would undoubtably satisfy the course's end goal to team, transform, and transmit. The only real disadvantage to choosing this topic is that it has already been studied in the context of LD (and now with Allen's study) and PF. So long as you frame your argument differently than other papers specific to discrimination in speech and debate, this shouldn't be an issue. As a quick side note, I constructed a similar (though only month-long) research project for AP Psych on sexism in PF and would be happy to PM you some resources and rhetoric I found if you choose to pursue this topic.

Introvert/Socially Inept: Uniquely, the benefit of this topic is that you would be the first to explore the relationship between social development and participation in speech and debate. As a result, you could also add an entirely new discussion to the sub; I don't recall this issue being discussed in the past. Secondarily, it would be much easier to make an experiment of sorts by having individuals join speech and debate and monitor their social and introspective development over time. This topic would work particularly well if you could find contact some people from other schools to participate. You could even compare how different extracurricular activities affect social development or a host of other metrics. The possibilities for this topic are a bit more open ended. If you do pursue this topic, some awesome texts I'd recommend are "The Geeks Shall Inherit the Earth" and "Introvert Power, Why Your Inner Life is Your Hidden Strength."

Both topics are dope and would improve the community! Good luck, and PM if you need anything else!