Letting the facts speak for themselves
Being able to make up lots of alternate stories is not the same thing as having an open mind.
An open mind means taking in the facts without prejudice and holding them in mind gently, without forcing them into a particular configuration. If the facts slide into place like puzzle pieces and create a compelling story, an open mind recognizes the merits of that story but doesn't become attached. Open minds can do this because they can withstand the tense discomfort of not knowing when they in fact do not know.
Another, very popular, approach that is labeled open-minded is trying to see things from many different perspectives by making up ways that people with different motives would be motivated to interpret the facts. Personally, I do this when my fear of being criticized is greater than my desire or courage to seek the truth. It feels crucial at those times to anticipate what everyone else might think, and I lose the backbone to focus simply on what's true. Coming up with dozens of defensible storylines is, in my mind, forcing the facts into dozens of more and less uncomfortable positions. It isn't waiting for the facts to tell the story. It's smashing puzzle pieces together and then reading the jumbled image like tea leaves. Although it could be a helpful exercise for exploring your own and others' biases, coming up with stories from different angles and levels of bias doesn't mean you're canceling out bias, and canceling out bias doesn't by itself mean you're getting the truth. There's no way you can account for all important bias in this manner-- how many alternate stories can you keep in your head?-- and biased or motivated reasoning is not the only obstacle to finding the truth. Trying to neutralize the prejudices of different perspectives just leaves you with a compromise between human biases. That position would certainly be less partial, but I don't see why we'd suppose it was accurate.
No, I believe our only guide to an unbiased version of events is to be motivated not to warp the events. If you can't make a proper puzzle out of the facts at hand, then you probably just don't have enough pieces yet, or the skills to assemble them. Of course, even when keeping an open mind, you will still have biases and motivated reasoning. Different perspectives are crucial to check your biases, but they should actually come from other people, reasoning with an open mind, and not from your imagination. Let's have lots of different people trying to find the truth, instead of everyone trying to guess what storyline everyone else will see and shape their storyline to consensus.