Things to do
If we can work out the distance along the ground the ISS appears to take, then on a flat Earth that easily tells us how much distance it covers ..
Calculate a minimum altitude, and from that an estimate as to mass to work out what forces (at a basic level) would be needed.
Relatively easy to do, assuming you have some rudimentary observing equipment.
Some web sites (like heavens-above.com) give accurate data on the predicted track of the ISS at a location. For this exercise, it is immaterial how the calculations are made, and what model is used to generate the data. The only thing that matters is that the resultant data reflects what actually happens.
Verify for yourself that the data is roughly correct. That is, generate an ISS pass prediction, and observe with telescope or binoculars on a mount with azimuth and elevation circles that 1) the ISS reaches the same maximum elevation angle as the prediction within about a degree and 2) the time at which it does so agrees with the prediction within about a second.
Do this as many times as it takes to convince yourself that the data is correct. Depending on how paranoid you're feeling, make predictions for different locations (at least 10 miles away) and repeat. Have trusted friends within 50 miles or so perform the same measurement, if you have any friends you trust.
Choose a prediction where the ISS will be going directly overhead. Station a trusted friend 50-60 miles along the predicted track. (I assume you can trust car odometers to be able to tell when someone is roughly 50-60 miles away so you don't have to use Google Maps.) Record the time at which the ISS goes directly over your location. Have your friend record the same, or be on the phone with him at the same time (that way you can verify you're both seeing the same bright object traveling the same direction). 50-60 miles divided by time gives ground speed. Don't worry, the difference between flat earth and round earth will be a small error in this calculation.
At another time, choose a prediction where the ISS goes directly over your location. Station a trusted friend 50-60 miles perpendicular to the predicted track. You verify that the path takes it directly overhead (90 degrees); your friend measures the maximum elevation angle. Using basic geometry, calculate the altitude. Again, flat versus round makes only a small difference.
Since I have been using predictors to spot and track the ISS for decades, and the results have always turned out as predicted, I trust them and can use their data to make a preliminary calculation of speed and altitude.
Ground speed: About 5 miles per second
Altitude: (Flat Earth) 264 miles (Round Earth) 245 miles
If you don't have friends to help you, choose any predicted pass to make these calculations, and spot verify with observations from one location or the other. Repeat as often as necessary with different path locations and observer locations to convince yourself that no one can be "faking" the predictions.
Even if you want to put unnecessarily huge error bars on these observations (a situation that can be remedied by statistics of multiple observations), you're still left with an object with a speed in excess of a mile per second and an altitude in excess of 100 miles.
That what you're looking for?