Hello- I have a 2009 mazda 5 with 205,000 miles on it.
I had some work done by my dealer recently:
-6 months ago, brake job.
-3 months ago, oil change/tire rotation. I drove off feeling a vibration in the front end (reminded me of driving on a cobblestone street) I figured the brakes were still new and needed to be worked in a bit more. a few weeks later, I had a nail in my tire and I took it back in to get the tire plugged.
I asked them to take a look at the vibration issue. They drove it and told me "everything is fine".
This vibration is ongoing. I should mention a while back, the "engine splash guard" (located between the engine and the pavement) was removed because it was damaged. I'm thinking this has something to do with this vibration? Any ideas are welcome!

 

Does this vibration occur only when you apply the brakes? Or does it happen while you are driving? Does it get worse when you are on the freeway? With my 2007 Mazda 5, I found out the vibration was caused by new brake rotors that were not trued properly at the factory. Once my local tire dealer trued my rotors, the vibration immediately stopped.

 

Bent wheel or out of balance tires, especially since it only occurred after a tire rotation was performed.
If you hit a sneaky pothole at one time or another like I did once (damned thing literally cropped up overnight and bent a wheel,) it may have bent a wheel in the rear which wouldn't be as noticeable except that now that wheel is on the front.

 

Belly pan doesn't make any difference to steering feel (but replace it anyway because it protects the engine/transmission).

5s are very tempermental about their wheels and suspension. Probably out of balance wheel. You should have taken it immediately back to the shop when you noticed the vibration and tell them "it an't right". Then they would probably have fixed it (re-balanced the wheels) gratis. Now you'll probably have to pay for it again, because they have no idea what you've done to the car in the months since you drove off.