1986 Mazda 626 problem.

Check underneath between the trans and engine for oil. Could be oil on the pressure plate. Make sure the clutch is properly adjusted.

Check for oil on the bottom between the engine and transmission. A leaking rear main seal can soak the clutch components with oil and cause slippage and chattering like this.

Also, when it lurches as described, what happens to the engine speed?

Ok. That tells me the clutch is slipping. Either the clutch disc and pressure plate are oil soaked, the clutch needs adjustment (I'll look for adjustment instructions), or the clutch disc is worn out.

On 626 models, clutch pedal free
play is.43-.67" (11-17 mm). Play is set at release lever. Depress release lever and pull roller
while measuring gap. On 323 models, clearance between release lever and roller is.06-.1" (1.5-
2.5 mm). On 626 models, clearance between release lever and roller is.08-.12" (2-3 mm).
1.
2. Turn adjusting nut to obtain clearance. Tighten lock nut. See Fig. 4.
On 626 models, adjust the installation length of the clutch pedal assist spring located at the top
of the clutch pedal. Turn adjusting nut to bring spring length to 1.14-1.54" (33.5-34.5 mm).

Check that distance from floor to center of pedal pad upper surface is within specification when clutch
is fully disengaged. On 323 models, standard distance is 3.3" (85 mm) or more. On 626 models,
standard distance is 3.2" (80 mm) or more. See Fig. 1.