In order for any driveline or steering system to be vibration or oscillation free, there are two constraints that must be met: The input and output shafts must be co-linear in all planes (front view, side view and top view) they don't have to be co-axial (in line with each other). This implies that the included angles at the ends of the inner shaft are equal. If they are not co-planar, then a phase angle must be added to the inner shaft of a Cardan joint set in a constant velocity arrnagement in order to cancel the secondary harmonic. Of course, the yokes of the inner shaft must be aligned with each other (can't be 90 degrees off).
If this can't be done, then a CV joint can be added to the driveshaft to eliminate the rotary harmonic. There are several types of Constant Velocity joints, each with a cost penalty and angular movement limits. In your case, either the transmission is tipped or the axle pinion nose is. Sometimes people forget that these requirements also apply under load, so the transmission movement or (more likely) the axle pitch during acceleration is the cause of your problem.
This principle applies to tractor driven 3pt hitch implements, too. For example, some implement manufacturers offer a CV driveline kit that ensures the input and output angles are always co-linear and some also specify a drawbar pin location so that the angles are equal. My hay equipment needs a CV arrangement from a Double Cardan prop-shaft for making the 90 degree turns in a field. If I use the wrong hole in the drawbar, the baler drive chains chatter. My F-935 front mower will chatter when I lift the deck because the output shaft is at a large side view angle relative to the transmission shaft. I have a Kuhn combo hay tedder/rake. You swing the main frame to change modes from tedder to rake. It used to have a CV joint at the rake gearbox but the previous owner damaged it. I replaced it with a standard Cardan type double cross system, BUT, it chatters horribly when I raise it up. I'm going to fab up a CV shaft insert from a FWD car axle to fix this problem. A new generic CV shaft is about $1000. The junk yard axle was $10.
