This is interesting. It sounds like my 94 Mazda 626... coincidence that Ford owns mazda, and the Mazda 626 engine is the same in the Ford Probe from '94. Not sure if it will help, but I'll tell you what the mechanics told me.
My car was 120k. I went to about 8 different mechanics, but had no work done. 1 of them told me it was a valve-train issue. That would be very bad. Basically, my valves were bent??? If that was true, then my engine would die. So I went elsewhere. I heard a few other stories, but 4 of the mechanics told me the same thing... after 100k miles, the cams need to be adjusted (dialed down?). They said that after that many miles, they just weren't lining up quite right and would make some noise. They also told me that it was not harmful to the engine and I didn't need to worry. It just reminded me of a bomb waiting to blow! TICK TICK TICK TICK. I never had a problem with the engine though, and since it was overhead cams it would have been a simple fix to pop the cover and adjust them.
It always seemed worse in hot weather. Honestly though, I noticed other cars doing it too! Expecially older Audis.
I was already planning on buying a new car though, so I didn't have work done. I'm sure this didn't help much, but it's just something to think about. Dang man, that's a 13 year old vehicle. It's time. Think about this though- It must really disturb you. I know my Mazda disturbed me. I also kept an eye on the gauges all the time, and it saved me more than once. I had a problem with the water pump 2 times. Well, 1 time the water pump died, so there went my engine cooling. But the 2nd time I lost a belt, and the belt is what turned the water pump, so I lost my cooling again! The exhaust system died 2 times, and that was $350 each. And one time I had a problem with the oil, in which oil got all over the motor. They had to decontaminate the motor and install new wires and whatnot. That was about $300. That was when I got fed up and decided to get a new car. If any of that sounds like you, you know what to do my friend!
P.S. Don't waste your money on a diagnostic. If your check engine light is not on, then there's nothing for the engine to report.