Max, that number 34199 is a tracking number used internally to keep the yoke and frame together, it's not the serial number. The number that you found on the butt of the grip frame is the true serial number.

As for a specific date on when the gun was shipped, you can only obtain that by having the gun "lettered" which is done by the S&W Historian by looking at shipping records. Cost for that was 50 dollars last time I heard.

Unfortunately, without a "letter" we can't identify the specific time frame because S&W will run a large lot of frames, stamp them with serial numbers, and work off that bank for years. In some cases I've seen reports of guns being assembled and shipped up to 15 years after the frames were made.

What you've been told is that the best estimate is that model 10 was produced in the 1969 to 1970 time frame and that's about as close as you can get for a model 10 without having it lettered.