If you 'dance' a bit on the clutch pedal, does that mimic the surge or jerk you feel?
Any differential with wear would generally show the wear in the bushings the spider gears ride upon, moreso than the actual gear teeth. When in straight line motion, the spider gears in the differential are not rotating on their shafts, they are sitting still. As redoctober mentioned, the spider gears will be moving when driving in a circle, and if they were skipping teeth, you should notice it more. Also if the spiders were worn, or loose on their shaft, or the shaft loose in the carrier, you should notice something with one wheel jacked up and the other held still. In that condition, rotating the wheel will rotate the spider gears, walking them around 100% of the time, as if one wheel was totally slipping, and would drive the input shaft & pulley at more than normal speed. You would/should feel if there was any 'give' or 'slippage' of the spiders.
If you inspected the spider gears and shafts, and the differential in general, and found no wear, or minimal looseness of fit, it should not skip teeth. AND, when it did skip a tooth, you would feel a 'jump' or 'bump' as the gear accelerated past the skipped tooth, and banged into the next one where it finally grabbed, and imparted more motion. It would not be a smooth slippage, but more of a 'bang' or the grind of teeth.
If you ever shifted a manual transmission, and didn't get fully engaged, you would have felt the teeth of the collar grinding against the teeth of the gear. When you finally get it into gear, unless you are quick with the clutch, you'd feel the slight bang as the teeth engaged.
If you haven't I would be sure to lubricate all the clutch linkage, and make sure the brake cross-shaft(left to right side) and the lever on the side moves freely. It should apply and release with not jerkiness or hesitation. If that moves, then check the clutch engage mechanism for free motion. The spring could get out of position and bind, making the cluch(belt) slip...