Remember when it was OK to have your dome light come on when you opened your door and turned off when you closed it - AAHH the good ol' days.

I guess you've already realized that LEDs don't dim (that's the Diode part of LED) and that you're OK with that. You are only concerned with the buzzing of the relay.

Your dweebish EE friend (I can say that cause I are one) was on the right track with removing the capacitor. Before you remove it though, you might just try putting a BFC (Big F%%%ing Capacitor) across the power leads of your relay. It should hold the switched voltage long enough (in theory) for the dimming action to finish and then bleed off fast enough so that the switch in the relay doesn't 'bounce'.