Low speed up/dowm shimmy

Hi, newbee here 2000 cherokee sport 4.0L auto4x4. This one has a slight but VERY annoying sea/saw up/down alternating motion (right side up-left side down then left side up-right side down) in the front end from 1mph on. Seems to increase with speed and never stops.
I just purchased this jeep monday and appears to be completely stock. Ive researched all the "wobble of death" threads and ALL those start at 50ish mph, not like mine.
My question is, does this starting at 1mph point to a different (more specific) problem or is it a variation of the "WD".
It has 2 new 8-month old tires on the front and other than that I know nothing about its past service/upkeep. It shows NO signs of ever being off-road.
Thanks in advance for your replies and this site is a GOLD MINE for new guys like me!!

Bent rim? Out of round tires (flat spots)?

Is this a different problem than the Death Wobble being that it starts as soon as jeep starts to move... not 50ish mph

Sounds like a separated belt in a tire

Three possibilities-
1) Both front axle u-joints are bad and are binding up and then releasing.

2) The Tcase is partially engaged in 4x4. Exercise the transfer case shift lever and the t-case and see if it loosens up and engages/disengages better. Find some grass or a gravel road. Engage 4wd high, drive a bit, engage 4wd low, drive a bit, shift back to 2wd.

3) Some sort of tire/wheel problem. Rotate one front to the rear, test drive, rotate the other front to the rear if needed. One or both tires/wheels may be the problem.