The Catholic Worker movement probably has a lot of what you're looking for.

Here's an example of one of their houses. I have spent a bit of time helping these guys fix up their buildings.
http://cherithbrookcw.blogspot.com/

http://www.catholicworker.org/cw-aims-and-means.html

To me, this is setting up a false dichotomy; that being, rational thought vs biased thought. Or said differently, rational thought automatically chooses against what a bias would choose. Said even more differently, thinking rationally isn't taking the opposite of bias. I think bias and thinking are happening on different planes and interact in weird ways.

As an aside, I find it extremely strange to say "aware of one's own biases". Bias is all about decisions that happen, seemingly outside our awareness. Decisions we make for what we think is one reason but is really a different reason, and our stated reason is a mere rationalization. If I were aware of my bias, I would take steps to not make that decision and would therefore no longer be biased, except in ways that I was currently unaware.

An example: let's say I'm biased against hiring women. In the company I hire for, I hire men way more than I do women, if I hire women at all. I could even be outspoken about this and claim that I don't believe women are as effective workers as men. This statement does not mean I'm aware of a bias, it is a declaration of belief. For me to be aware of my bias means to acknowledge that my belief is incorrect and leading to negative outcomes.

I can't effectively model a person who is aware of their own wrong belief (bias) and still chooses to believe it. (I'm aware I want to buy that shirt because the store placed it at the front, so I'm going to buy it anyway for that reason) I just don't see that happening. I think we can only acknowledge that bias might be happening and needs tested.

Back to original train of thought with this understanding of bias. Bias comes to conclusions based on processes that are not the evaluation of available data. Confirmation bias is seeking only a subsection of the data available. The reason we do this is because convincing ourselves we are right feels good. The decision here was made not by thinking, but by feeling good. Confirmation bias just might lead to the right conclusion. Bias does not guarantee rightness or wrongness and that's the issue.

As to the survivorship of biases, it doesn't really make sense to believe that only useful things survive and all negative things die off. Surviving is about lasting long enough to reproduce which means only items with severe and quick consequences die off. Benign errors or slowly acting errors can easily survive while serving no beneficial function. Many of the fallacies fall in this category. They don't lead to immediate death, therefore there's no mechanism to get rid of them. Sunk cost is wasted effort, not seeing death in that. Revenge either happens on a level less than death, or so rarely that it doesn't impede population growth. The marshmallow test doesn't look like a bias, just experiments. It's never a good idea to take a single study as truth, but unfortunately the social sciences do this a lot.

I think we also need to consider the dangerousness of the environment. Really harsh environments don't tolerate many mistakes and so organisms that live there are much simpler. More complex organisms have way more opportunities for mistakes and you find them in gentler environments. This feeds back into surviving long enough to reproduce. Errors and mistakes don't have to serve a function to exist, they can simply be tolerated in a gentle environment.

I think I interpret this phenomenon as a motivation problem. The fear of letting someone down is more motivating to you than the actual task itself. We are inherently social creatures so this makes a lot of sense for why it's working for you. I'm not sure I'm really getting the connection to morality.

Maybe there's a need for more clarity on what morality means. Does moral just mean BAD or is moral a substitute for "damaged social connections"? Are you more motivated by not being BAD or are you more motivated by keeping your social connections strong?