Jerking

I would check the drive axles for any issues. They could be binding under the right conditions. Do you hear anything when it happens? Does the engine seem to stay at the same rpm and power when it happens? Where do you feel it the most, in the steering wheel or in the seat? The hard part is that it doesn't do it constantly so tracking it down could be difficult.

Pulling right and in feeling it through the steering wheel would lead me to the right hand axle shaft as the problem.

Please let us know what you find. We are interested to see what it is.

I seriously doubt that as there is no way air (which is 70% nitrogen) is going to cause a jerking issue, It has zero weight. The only reason they say to use nitrogen is that it
A - Has a predictable temperature curve which is useful in racing.
B - Is a dry gas when taken from a tank. That means no moisture like you can get from plain
air if it is humid or from a compressor that hasn't been serviced.
C - Costs more to fill a tire with than air.

However you might have an issue if something fell inside a tire while they were mounting it. A loose weight or even a chunk of dirt can do strange things if it's inside a tire. Easy check would be to put the tire on a balancer and rotate it by hand to a random spot, mark it and then spin it up. See where it says it needs weight. Mark that spot. Now move it to a random spot and spin it again and see if it stops at the same area it said you needed weight on the first run. If it's different there is something loose in the tire. Or just break one bead and check for something in the tire.
To act as you describe there is either a mechanical issue with a bearing or axle shaft or there is something inside the transmission that is damaged like a broken tooth on the final drive or similar.