Jason, I would have been okay even with your first 0.006"-0.008" clearance. Optimal tolerance for used parts is 0.004"-0.010", measured between the built-in output shaft thrust and the 3rd speed gear. A true, square gear read of 0.003" is actually fine.
What you describe as a "low spot" would be called a "high spot": You get a 0.003" read all around and 0.004" at all points except a small section with a high spot—meaning that at that point the thrust to gear face gap is tighter due to something protruding at 0.001" or slightly less. Make sense?
Actually, I don't think you have a high spot at all but rather a gear that rocks slightly on its bearing during gap measurement. A suggestion: Measure with the feeler blade laying sideways to the gear as depicted in OEM shop manual views. By dipping the feeler blade tip straight into the gap, you get slight variances due to rocking the gear on its inner bearing. A side blade read tends to keep the gear square, which is the only way to read gear endplay or the gap accurately.
If you were "blueprint" building this gearbox, you could slide the gear as squarely as possible along the shaft and read "endplay" between the thrust and gear with a dial indicator. Another way to do this is to measure with two feeler gauges placed opposite each other between the thrust and 3rd gear. That will prevent the gear from rocking on its inner bearing.
A slight high spot of 0.001" or less (which I don't believe is the situation) in one small area of the thrust would not be a great concern, as there is a protective oil film between the thrust and the gear. Good gear tooth alignment with the counter gear and correct synchronizer ring gap matter more. Again, the close thrust gap, with the original snap ring snugly in place, indicates virtually no wear at either the thrust or 3rd gear face.
Note: When you say that the snap ring is "snug", it must be snug in terms of endwise movement while seated fully in its groove. There should be no measureable gap between the snap ring and synchro hub with the snap ring fully seated in its groove. The snap ring width is selective fit for that reason.
Back to your original assumption: To determine the location of any high spot, hold the shaft steady and move the gear in 45-degree rotations. Keep measuring the gap at the same spot on the thrust. If the gap changes, any wear or machining error is on the gear mating face, not the thrust. Judging by the snap ring and synchro hub fit, there is plenty of thrust material left to keep the gear aligned properly, and the oil film will protect against friction damage.
For a correct gap reading, I would press the synchro hub evenly onto the shaft with enough force to seat the hub squarely against the shaft shoulder. The original snap ring filling the groove snugly at this point indicates no appreciable wear between the synchro hub and shaft shoulder—and that's great. The measurement between the 3rd gear face and the output shaft thrust face is normal at 0.004" and just fine at 0.003".
The hub will not creep, and the thrust gap allows plenty of oil between parts. 0.003"-0.004" indicates virtually no wear since the OEM build. If there is no snap ring-to-synchro hub play, and the snap ring is snugly seated all around the groove, your transmission is doing fine here, Jason!