Neither gun posted can conclusively be called factory 2"bbl. Police Positive Specials because they both have the wider 1 7/8" square butts, instead of the older narrow 1 9/16" square butts. The butt configuration is just as an important feature as the barrel markings are. The wider square butts were introduced in 1928. The SN quoted by the original poster is also from 1928. Some "Pre Detective Specials" were shipped by the 2nd quarter of 1926 and all of 1927. By 1928, the revolvers had wider square butts and were officially called Detective Specials. They had a serrated matte top strap sight channel, a checkered trigger, the wide square butt, and the iconic pre WWII 38 Detective Special barrel stamping.
I see the barrel would be correct for a factory 2" bbl. Police Positive Special, but it could just be a left over 1927 barrel which Colt used on a first year (1928) Detective Special. If the 2nd gun doesn't have a narrow square butt, a smooth top strap, and smooth trigger, it is not a "Pre" Detective Special despite the correct barrel. We can't see the top strap or the trigger in the pictures. But without seeing them, the barrel marking alone doesn't make the gun a "Pre" or transitional D.S. model. We need pictures of the aforementioned parts and the factory letter.
With the wide butts, I don't think they will have all the correct criteria.
Criteria and dates, etc. are from Gary Peer's excellent " The Colt Double Action Snub-Nose (Pocket) Revolver" book, and my own humble observations collecting these guns over the past 10 years.
As I mentioned earlier in the thread, it's most probably 1st year Detective Special with a year earlier barrel. Still a valuable Colt, but not the same as a "Pre Detective Special" aka factory 2" bbl. Police Positive Special.