Although I do not have first hand knowledge, I have heard from my chaburah that the Lubavitcher Rebbe many times gave shiurim or pilpulim that showed how the multiple seemingly unrelated machlokes between certain ta’anoim or amorim was based on a common thread li’shitasom. (Examples: if we view the matter generally or in detail; if we look at the act itself or the outcome etc.).
From what I heard, these insights were mamesh gaonuss!
This was also the approach of the Rockatchover Gaon in various machlokes in shas.
If you know someone familiar with this godol’s Torahs in this area, such a person can assist you.