Mazda - Mazda3 :: Intermittent Vibration Mostly On The Floor But Sometimes Also On Steering Wheel

I have a 2008 Mazda3 (2.3L automatic, 34K miles), which has recently been annoying me.. The problem started about 4 months ago, when I got new tires and a brake job (pads + rotor resurfacing). Ever since, it has been having intermittent vibrations. I feel the vibrations mostly on the floor, but sometimes also on the steering wheel. Here's what I've done so far:

When the vibrations started, i thought it was a problem with the new tires. I had them re-balanced 3 times at two different places, with no improvement. I then took the car to the dealer, who replaced two of the three engine mounts (it appears these tend to break easily on this model). This seemed to improve the situation for about half a day, and then it went back to the same. I took it back to the dealer, who could not find anything wrong. Not being satisfied, I took it to a different dealer, who could also not find anything wrong.

So, I am now stuck with this vibration.. It is not always there, and not always of the same magnitude... it seems to be more likely to happen in the morning after a colder night (well, as cold as it gets in Los Angeles). It is most likely to be felt at around 45-50mph, but you can also feel it at higher speed sometimes. A couple of times I could definitely feel it at around 25mph. Also, I've noticed that the engine vibrates when the car is stopped, at around 1500-1800rpm (e.g. when I first turn it on). The dealer claims that this is natural for a 4-cyl engine, but I had never felt a vibration before.

My gut feeling is that this is something related to the engine, but two different dealers could not find a problem... since this is intermittent, it is hard to nail down I guess.