I've got one coat of polish and 3 coats of protectant on. Can I just put another coat of polish over the protectant? Or do I need to get rid of the wax?

 

You didn't mention how long it had been since you last applied the polish and protectant. Both will erode over time. I usually clay, polish and apply protectant 2-3X annually. But if you're trying to get a better shine, you'll need to strip the car down and reapply the polish first.

 

I did one complete coat (polish and then protectant) 3 weeks ago when I firt got the Z. Then, I put on two more coats of protectant since then.

The reason behind all this is I've noticed some more swirl marks appearing. I'm thinking they are in the protectant. I'm using all microfiber towels to dry the car. My wash mit is also soft microfiber.

 

Swirl marks are another issue (one that I personally don't worry much about). You should do a search in this forum on that subject and get some additional recommendations.

 

They are very light. This is why I think it's in the protectant.