Your attempt to harmonize the different chronological data in Daniel 1:1 and Jeremiah 25:1 is a joke. You already have admitted that tthese statements are not of the same historical event but you believe that these occurred in the same year because of th accession and non-accession year system used by Jeremiah and Daniel. However there is a big problem with this argument which remains such even to this very day. Although in principle Bible writers used this system for chronological purposes its application today is not fully understood and universaly applied.
There is no big problem. Daniel lived in Babylon. Daniel was taught in the ways of Babylon. Babylon used the accession-year system. Therefore the most logical answer is that Daniel used the accession-year system.
Scholars such as Edwin Thiele certainly recognized the principle or method but scholars like Thiele disagree as to the method of application. For example, there is no consistency of its use during the Divided Monarchy with the kings but it varied for the kings of Judah and Israel and varied at different times during the overall period. The apparent lack of uniformity in its application renders its use in the modern day setting extremely vexatious. For this reason celebrated WT scholars have chosen rather than a reganl based approach but rather the more practical-event based methodology for this removes to some extent the varaibility of the accession and non-paccession principle.
Regardless of the variant use in Israel during the period of the DM, there is very strong reason to suggest that Daniel used the accession-year system. To suggest doubt about which system was used during other periods of the DM is a red herring.
Point number two is that Daniel did not use the word reign but kingship as properly translated so the interpretation of the third year is shifted from a regnal year to an historic event in the course of his reign of which was in fact a kingship as a vassal to Necho and Nebuchadnezzer.
Daniel didn't speak English. He didn't say 'reign' or 'kingship'. There is no distinction in the Hebrew word used. The two English words mean the same thing.
1. Different history
Only different in the warped minds of the Society law-makers
2. Inconsistent methodology
No inconsistency has been identified.
3. Diferent Hebrew term as kingship rather than reign
Both words mean the same thing. It is the same original Hebrew term. The Society does not always translate the term as 'kingship'.