So, that problem of needing access to scholarly databases to which your institution doesn't subscribe? I may have found a solution.
Register as a nondegree or nonmatriculated student at whichever local institution does subscribe. Obviously, not all universities permit students in this category--I imagine you can't be a nondegree student at Princeton--but plenty of places whose mission involves the surrounding community have programs that allow random citizens to take a class now and then on either a credit or audit basis. And in my experience at two institutions in two states (Cosimo's public R2 and now a private R1), all you have to do is fill out a quick web form, wait a day or two for approval, and then you get a student ID number and login.
And that gives you library web access.
Now, I can't promise that every institution would give you library access without your actually enrolling in a course--or that such access would last for longer than a semester or two--but in both the places where I've been a nondegree student, web access to everything was immediate, and not a function of being enrolled or paying one red cent.
I leave it to the enterprising among you to conduct further research.