lateral shakes
I thought that it was well known that any aircraft with the thrust distributed across the wings hundreds of feet apart, can be prone to minor lateral accelerations, or “the shakes”, most keenly felt near the tail. I have heard flight crew announce many times over the years to expect some sideways movement at the back because of a tail wind. It was most noticeable on 707s for some reason, but is also evident on 747s and 340s. I think it was referred to as ‘tugging’ or ‘snatching’, or something like that.
Like the OP said, it can be very jerky and tiring at the back, but it is hardly noticeable around the centre of the aircraft, and by the time you get near the front you can feel the effect but the severity is well damped. I am not a pilot nor have I worked aloft in any capacity; it would be interesting to hear about this from someone who has.