Wish I had mod points.
Open-sourcing the data and process might help with overcoming those barriers. I don't know much about climate, but I deal with big dumps of numbers, and turning them into useful graphs and charts, all the time. If I could go to a place to get the data, I could possibly leave you more time to handle the simulation processing (and understand it better), and the data-collector more time to set up/check/confirm data (and understand IT better).
(BTW, for four-dimensional arrays, do you just mean that there's a point on a map, a point in time, and a depth for each measurement? Or are you dealing with other dimensions as well?)
Of the others
1) Computing power. Not sure how to get around this. Sure, could do some distributed computing, which people might be more interested in with more transparency.
2) Big data dumps, representations of: LIke I said, possibly a good place for division of labor anyway.
3) This is probably where transparency is needed the most. People might be okay with the fact that it's complicated, if they can dig in and see what the factors are, and at least come to an understanding about it.
4) Sounds like more of the same as 3 - assuming that analysis largely includes the stuff that was too complicated even for the model.
Your "go look for them" is easier said than done. When I look around to check my honest skepticism, I end up at sites that are, well, polarized. It seems like either they have absolutely no doubt about what's happening or they have no doubt that it's NOT happening. In either case, it's hard to feel comfortable with their conclusions. And if someone does answer my big question ("The Vostok ice cores show previous cycles of warming, even more than we have now, soon followed by ice ages, so why is there a belief that This Time It's Different?") I have to figure whether they are biased, and how that affects their answer.
Which brings us back to TFA, and how polarization between the camps needs to be dealt with, so that everyone CAN agree on What The Science Says, regardless of policy prescriptions.