I'm doing some work with sports statistics where I need to evaluate at what times part of the field is covered by shade. I already know that shadows cover the portion I'm interested in from roughly 4:33 EDT to 5:00 EDT on 4/28/22 and from roughly 4:51 EDT to 5:26 EDT on 5/22/22. Is there a mathematical way of estimating the time/length for other days based on the known values? Any help would be greatly appreciated.
Not certainly, but some fiddling with Suncalc.org suggest that your shadow starts when the sun reaches an altitude (angle above the horizon) of 36 degrees in New York, and leaves when it reaches an altitude of 30 degrees.
Here's what I did. I set the location to 40.78, -73.87. I then set the times in your question, and noted that the azimuth (bearing) of the sun was very different at those times, but the altitude was very similar (36 degrees). This might be the case if the shadow is caused by a some horizontal stands. You can use Suncalc to find when the sun reaches 36 degrees and that will predict the time when the shadow will start.
For example, this model predicts that the shadow will start at 3:00 EDT on October 1st, and continue until 3:44.