Another success route here involves finding Professor Foo of the Interesting Funded Research sometime in the fall or spring, telling Foo that his research is cool, and then asking if you could you help out (volunteer). The answer will likely be "yes", and then, providing you're being a relatively functional person, you're now a strong candidate & provisionally in the rotation for the next blob of funding coming along.

(This has happened in multiple scenarios to various friends and self).