I thought Hague produced Republic and wrote quite a bit of it with Sumner, but was not aware he had such a great hand in Regret... that seems too guitary for him...
the problem with this type of list is that there is a huge grey area between coproduce, produce, and cowrite... when bands are in studios, nothing is that clear usually, where ideas come from, how they are implemented, etc...
it IS more clear when a band walks into a studio with material already all penned in their own rehearsal studio (and sometimes even demo tracked even) - but with new order, they usually showed up in studios with nothing really, take their time, have a few ideas that are then fleshed out by Baker or Hague, etc....
often there are no obvious ways to determine just how much help they got. and no way to ever discern the truth, as everyone has a different take on it... Hook may think his bassline made the song come together, or Morris may say his sequencer line was the inspiration, or Sumner may think his lyrics made the song work... or Hague may feel that his production, his ideas to lengthen a chorus, chop off a verse, were what made the song publishable....
but I do admire you for compiling all this and trying! very interesting.... makes you realize just how much goes into putting together these lps...