I think the question is very interesting, but a bit difficult to answer due to a lack of detail and accuracy in data dating back from pre-atomic clock era. Also, we have to decide which type to day to analyze, mean solar day or apparent solar day? From the elements in your question, you seem to be describing the mean solar day, so let's analyze this one.
One thing that we can notice in several studies, such as this study by Morrison and Stephenson, is that the length of day (LOD) was longer on average around 1900-1915, with an average day length close to 4 ms longer than 86,400 seconds:
Before 1900, the tendency is really towards shorter day values, so I think it is logical to assume that the beginning of the 20th century saw the longest day values (at least on average), and that the longest day likely occured somewhere in that period, although I can't confirm this, nor can I confirm which day it was, because LOD fluctuates quite a bit, and data from occultations, transits and eclipses back then just aren't detailed nor accurate enough for such an analysis.
If we analyse the time period where daily data is available with good accuracy (approx. the last 60 years), on the IERS website, then based on this data, which includes daily values of LOD since 1962, and taking into account the margin of error, I think that October 31, 1971 and April 12, 1972 are the two contenders for the longest day for that period (highest LOD value between 1962 and today), with 0.004348s and 0.004355s respectively.
Here is the graph of LOD from the IERS website:
In the future, as you know, the days are expected to get longer and longer, so eventually, the record should be broken. How soon is anyone's guess...
Analyzing the apparent solar day would be much more complex due to several factors that affect the actual apparent length of the solar day, like the position of the Sun, planets, orbital eccentricity and axial tilt.