Hey Tom,
I just tried that a minute ago, attaching 104 from 5 to GND and a 470uf from Vcc to GND (I ran out of 100 uf).
It did not affect it, except the buzzing/whining sound starts of more articulated than it did before... I'm not sure if that is progress but if it is then cool! 
EDIT: Then I tried switching 1k to 10k. It is definitely slower, and the buzzing/whining noise is much lower. It sounds like the relay is stuck or something; some oscillation going on of course.
Thanks MAS3 for verifying that I can use this 555 timer!
Still not solved 