But what really gets me is the disconnect between "most scientists agree there is a reproducibility crisis" and "most scientists believe most of the papers they read are basically true and reproducible". This was mentioned in the survey and it conforms to my informal experience of attitudes.
I do not know how you square that circle. Maybe, because of the pressures you mention, we are all supposed to engage in an informal convention of pretending to believe most previously published work is true, was done correctly, and is reproducible even if we know damn well how unlikely that is. I find it hard to do.
One day the public is going to cotton on to all of this. I cringe every time I hear extremely authoritative lectures on "what scientists say" about highly politicized public policy matters. These are not my fields, but if they are as prone to error, bias, irreproducibility, etc, as my own, I'd exercise some humility. It is one thing for we scientists to lie -- errr, project unwarranted confidence -- to each other for the sake of getting grants, but it is quite another to do it directly to the public.
But when the public does figure it out, what do you think will happen to funding? It will get tighter, and make the problem even worse. We need reform from within before the hammer falls, and quickly.