92' Trans. shudder from 4th to 3rd on downshift

I recently inherited a 92' lumina (3.8) with 8,000 miles on a rebuilt transmission (out of warranty period). My problem is a shutter/slipping when momentarily slowing down from cruising speed (above 45 mph) and accelerating again. The trans. downshifts from 4th gear (overdrive) to 3rd gear. Once in third gear and I accelerate to regain cruising speed, the transmission has a slight (but noticeable) shutter and hesitation. If I accelerate hard to downshift to 2nd it stops. If I accelerate "slightly" to regain speed the shuttering only last a second or two and then sort of "kicks" in and shifts to 4th with no problems. Anyone have any ideas? I've drained some fluid out and added LUCAS transmission additive in hopes of a quick fix but it hasn't helped.

Welcome to AF, there was no 3.8 in 92. Anyway this could be an ignition misfire or it is the trans beginning to fail, someone knowledgeable should drive the car to determine the source.

I can't remember if that year still used a transhift detent cable for determining throttle position. Incorrectly adjusted cables caused what we used to call "overdrive search and lurch" where they'd kind of hunt around for the correct gear unless you stepped on the gas with some authority...

But I can't remember if they used cable detent on early OD transaxles...