Altenae, you've received a great deal of suggestions from other fellow forum members, however, it would be best if you had the vehicle inspected by a technician. My 01 Sport Trac had a similar idle issue since new, it never got worse, but it was never bad enough for me to do any more than to complain about it from time to time. Nothing that I did made that go away. It would idle very nicely most of the time, but from time to time it would send a series of inputs into the chassis, which I could feel inside the vehicle. It didn't look like much while watching the engine but it felt rough and unrefined.
In my humble opinion, Explorers are relatively low-tech and unrefined. Others will have their own opinions on this, but I've driven various types of vehicles, including SUVs to have reached this conclusion. You'll get to a point where you've exhausted every option and you still come back to basic and typical lack of attention to detail at the design phase.
Ride quality is a very subjective attribute. Suspension engineers calibrate spring and damper characteristics to suit a certain driving style and to satisfy the majority of consumer preferences. Hence, we all tend to assess ride and performance according to our own likes and dislikes. I found my Sport Trac to be nothing short of dangerous on the highway...never mind the dreadful ride quality. Most of the people that I drove around in it pointed it out and, even though I sold it already, they still bring it up to tease me. It's doubtful whether putting on aftermarket shock absorbers will smoothen the ride. Aftermarket shock absorbers are typically stiffer. They'll offer more control but will compromise on primary ride quality. Whatever you do, DON'T lower the tire pressure below the specified pressure (owner's manual or label on door jamb).
I'm sure you're well aware of the fact that the SUV will feel different from your sedan, you've stated that already. If you feel the ride quality or idle quality are at an unacceptable level, you should have a technician confirm that. You've done everything you could do and you've taken a logical approach. Without any trouble codes, it is hard to pinpoint what it could be. If it is mechanical, someone will need to diagnose it.
Someone suggested checking the engine mounts. The rubber portion of one of the mounts could have deteriorated - that will need to be inspected, however engine mounts are designed to absorb vibrations at certain frequencies. Beyond that, they're solid chunks of rubber whose ultimate purpose is to support the engine. I've had broken mounts before and the only time they got vocal was when going over bumps. A vibration is a result of mechanical or firing imbalance so the root cause will need to be investigated.
I'm not sure how hard it will be for you to find someone locally who is well versed and honest to disclose and diagnose the problem correctly. Don't spend any more money until you've had a conclusive diagnosis...that's my advice...
