Extreme Rationality: It's Not That Great
For me, the core of the rationality project is something like a determination to make your beliefs completely subservient to reality, at all costs, fighting your natural instincts for defending your beliefs, trying to win debates, etc. Not trusting your beliefs just because they are yours. Approaching the most controversial and divisive subjects with a curiosity mindset. Looking forward to changing your mind.
Most "normally rational" people can do this in technical and scientific matters, but in other domains, such as politics, philosophy, society, economics, religion and their personal lives (to some extent), such a stance is extremely uncommon, even among very "normally rational" and highly-educated people -- thus according to your taxonomy, it would fall under x-rationality, I guess (even though I'm not sure whether that's what you intended). In these areas, tribalism, confirmation bias, trying to win debates and talking past each other usually wins out.
All the other parts of x-rationality -- all the techniques and tools -- are just that, tools (of varying levels of usefulness, of course). I am not going to argue much for the value of the tools, mostly for the value of The Determination. When you have The Determination, you can seek out the tools you need.
The Determination is valuable in many ways.
People with The Determination make a better society, coordinate better, choose better policies because they actually listen to arguments from all sides and don't just fight with each other etc. And because high-level societal problems are messy and complicated, ordinary rationality is usually not enough. I know, this is not what you are aiming for, it is not a direct benefit to the practicing individual. But I think it is important and overlooked nonetheless.
Especially in light of the COVID pandemic, it is very visible how desperately we would need more Determined people. Even well-educated rational people such as doctors and biochemists sometimes spread dangerous falsehoods (and stuck with them) because they overlooked some simple fact (e.g. how an exponential growth really behaves). When confronted, they just rehearse their arguments, which make perfect sense themselves, except for the fact that they overlook a crucial consideration. When you have The Determination, you are always on the lookout for crucial considerations missed.
This is a tangible practical benefit (e.g. there would be much less dead) but it is a group benefit rather than an individual one.
As for truly individual benefits, I'm sure there are many, but they differ from person to person. For me, the most obvious one is that I can much better talk with people of widely differing opinions, I am much less confrontational and generally relate to others better. This has been hugely valuable to me.
It has also greatly helped me in matters of relationships and emotional regulation. I can for example handle my emotions in a similar way to my beliefs: not taking them at face value, treating them as a hypothesis. I can notice when I fall into harmful patterns, react poorly because of something completely unrelated, start forming an anxious-preoccupied / codependent attachment, etc. and correct myself, no matter how real it feels. This is the same mindset of never fully trusting yourself, just applied differently.
As for achieving mundane life goals such as getting jobs and money, I'd concede that x-rationality does not help that much. On the other hand, I think it can for example help you notice that you chose the wrong goals (e.g. you believe something will make you happy when in fact it won't; people are generally lousy at predicting what will make them happy). Again, the same stance helps. Treating everything, including what you want, as a hypothesis.