Shoot, I wish that you lived in Wisconsin so you could take a drive in my TM3, as you sound very knowledgeable! I feel like you could tell exactly where my vibration issue(s) is!
After my 2 road force balances, I feared that it was a motor bearing / drvietrain issue, but these days I doubt that. I've been waiting for a nasty winter weather forecast before putting on new Aero's with X-Ice 3's mounted, so that should tell me something as well. Right now I can still hear a low frequency chugging sound as I go above 55mph, similar to what you hear when you only roll a single window part way down (with no real vibration in the steering wheel any more). Does that help isolate what the issue could be?
If it increases with speed, there are a few things to check:
1. Flat spots on the tire (usually caused by emergency braking). These usually show up at any speed, but one that isn't very severe may show up only at higher speeds.
2. Caster angle. (Think of getting a shopping cart where the wheels go wonky, that's too much caster). Increases with speed and often doesn't show up until you get to highways speeds.
3. A heavy spot in the tire, possibly a very thick casing splice (Feel around the circumference of the sidewall, you will likely feel an indentation where the splice is. This is normal, but once in a while you will find two together (usually these tires are not sold as first line tires, but blemished tires--occasionally one gets through. I've seen some with as many as five). This will not show up as an out of round condition.
4. Too much wheel runout. The tire must be demounted to find this.
5. Too much balancing weight. There's an amount where more weight doesn't help.
6. Dynamic imbalance of the tires and wheels. The vibration goes in an out at speed, so for example if it starts at 55, stops at 65, starts again at 75 or 80, that could be the problem.
And some non-tire ones:
Do you have a roof rack on your S? I have seen cars that the roof rack causes a vibration, sometimes severe. I'd find that really odd on a Tesla with a glass or pano roof, but some were made with metal roofs and the air flowing past the roof rack could vibrate the roof.
Because you're describing it as if it were pressure buffeting, is there anything loose (like some of those plastic bits) underneath that could cause that.
I don't know what kind of animal could make that sound, but there have been instances of cats climbing up under the motor.
Some things to try:
Switch the tires to different positions to see if the vibration changes.
As you've suggested, put the winter tires and winter wheels on.
Do the pencil test (you'll need another person for this). Method: Get a pad of paper and a pencil or marker (not a ball point). One person drives to where the effect is felt (sounds as if 60 mph would be a good speed and makes for easy calculation). The other person taps the pencil on the paper in time to the vibration for a measured amount of time. (Six seconds is typical because you only have to multiply by ten to get the number per minute. You can also count for a full minute, but there may be hundreds of dots, so counting them is a pain). Do this two or three times to make up for the small variations in the six second timing. You now have the number of vibrations per minute (and at 60 mph it's also per mile). Match this with the rotational speed of various components (such as the tire revolutions per mile--available from the tire manufacture's specs on their website). If it doesn't match the revolutions of the tires, you can eliminate them and look for other items such as steering components, suspension, or something else.
Vibrations and noises in cars are often hard to pin down because they are often felt or heard in different areas then they are actually coming from. In the most difficult cases, sensors or microphones need to be placed in various places to actually determine the location.
