Sam,

I'm happy to give you some direction, but it would mean starting over from scratch - are you up for that?  Or you can stay with what you have so far and make something more like an aster or daisy.

If you look at this picture  you can see that the center of the flower is huge in proportion to the petals.  The petals have a definite overlap to them, rather than being side by side.  They also appear almost "fluted" or corrugated.  The other significant visual key is that the seeds in the center are arranged in a series of concentric spirals.

I'd suggest making two petal pieces so they can be stacked to get the visual density.  I'd make the center a separate piece with the seeds suggested by lines chased into the copper.  You could make a quick chasing tool with a "V" shape to suggest the seeds.  Start by doming the center a bit in a sandbag and then fill the back with plaster of Paris or stiff wax to give you something to work against for the chasing work.

You might also want to do a Google search for sunflowers to see what the leaves look like so you could add a couple of those.  If the piece is going to be viewed from all sides then you need to know that sunflowers have several sepals around the stem and the back of the flower is roughly a shallow funnel shape.

There you have it.  That's how I'd go about making a sunflower.  Here's an abstract one I did on the power hammer using heavy steel.  You can see how I just suggested the petals by using a tool to set down the steel so it looks like two layers of petals and the seeds are suggested by chasing lines in overlapping radial arcs.  This one is about life size, say 12" in diameter.

 forged sunflower