Interesting, yes DeepDyve looks exactly like what I had in mind. Thank you, will give it a try.
The other reply (no longer visible for some reason) mentioned the university library through the alumni association. I've gotten in touch with the library and received the following reply: "Due to licensing restrictions, we are unable to provide remote access to Research Port databases to alumni. Complete access to all of the Libraries' databases is still available through computers at any of our eight branches." . So it seems like the policy varies from university to university.
Haven't heard back from my local library yet - might stop by there tomorrow and find out.