When I first tried to learn Taigi, it was still CSB time, and back then the situation was even more chaotic. The TLPA came from scholars trying to address some of the issues that TL later addressed. Back then Unicode hasn’t been widely adopted, and tonal marks won’t be displayed unless custom fonts are installed, so TLPA was pushing for just writing the tones as numbers, while a number of other systems were pushing for using unused alphabets as tonal marks, such as f, r, x, like MLT. There are other systems that stray even further away from POJ, like using b for p, and p for ph, such as Tongyong.
So in 2005 the POJ people and the TLPA people (most linguists) figured it’s better if they work together and get a standard through. They scrapped the arabic number tonal marks from TLPA and got mored aligned with IPA, then replaced o͘ and ⁿ with oo and nn, since that’s how you would type them anyway.
While the system was being hammered out, it was just called the Taiwanese Romanization System, Tâi-uân Lô-má-jī Phing-im Hong-àn, hence TL. The Minnan part was added because the legislature will decide whether or not TL or Tongyong will be the system taught in schools. In the end Tongyong lost, and TL (POJ+TLPA) won.