Dielectric grease doesn't help make an electrical connection. It is nonconductive. Its purpose is to help seal moisture out of the connection, prevent corrosion and make it easy to disconnect the fitting even years later.
If you think the connection isn't tight inside, what you can do is use a pair of needlenose pliers to bend the male wire tips inside the plug just a bit. It doesn't need much, the idea is to put just enough of a bend into it to make the fit tighter. Give all the male tips a very slight bend in the same direction so the plug can still slide on. By slight bend, I mean like 2-3 degrees tops, or just enough that you can tell they're bent if you are looking for it but wouldn't notice otherwise.
I will take that advice and try it later today, I'm not sure why I was thinking dielectric grease is conductive, as soon as I read your comment I was saying duhhh to myself. I have two head units to work with too, I got one from a junkyard about 2 months ago, I figure I'll try it on that one too while I have it out and see what happens...