Your observations are very interesting, AlM, and so are your insights. You have rightly been congratulated for this initiative.
Some trains moved slowly into the station, and you attribute the fast moving by the remainder to the skill of their T/Os. But if any of those slow moving trains were running early, could the T/Os have been right to go slowly and/or linger in the station? Or is the rule to keep moving as fast as possible, regardless of whether you are late or early?
Which raises the question: which strategy would result in the greater throughput: keep as closely as possible to schedule, or keep moving as fast as possible? This question could be tested by simulations. The optimum strategy may not be so simple.
To find out if trains were early or late you would need a timetable, and some way to identify each train with one in the timetable. Otherwise you cannot even tell if they arrived in the right order!
It seems significant that in a sample of ten trains, several were delayed by "unfavorable events", all resulting in the doors not being closed soon enough. Variable numbers of boarding passengers are clearly a big factor.
You observed ten express trains and six locals. This suggests that the Lexington local is running below its capacity in rush hours. If the upper east side is so short of trains, perhaps they should try running more Lexington locals.