The thing is, Varis wasn't completely dismissive towards the death of his son. His statement begins with '...' which suggests a measure of hesitation and sadness. He even looks somewhat conflicted in terms of his expressions during the cutscene in question, though he also states that Zenos is a monster and unfit for the throne. Given that Zenos turned himself into an Eikon and Varis apparently saw that happening, it doesn't make much sense for him to keep someone like that around...especially when Garlemald's goal is to put an end to the Eikon threat. As for Elidibus, he clearly showed Varis something that shocked him - so it's not like the guy is without emotions.
Now, if Elidibus plans to bring about Zodiark's rebirth, him backing Zenos rather than Varis makes sense. Varis did not send reinforcements to aid his son and does not share Zenos' enthusiasm for mindless bloodshed. Zenos, however, is completely unhinged - and it could very well be the case that Varis and others in Garlemald could not overpower Zenos through conventional means and thus sent him to the outer territories hoping that he would be killed in combat. Varis is, after all, described as an excellent tactician...
Varis not being present in the ending is suspicious, too.
As for Asahi, if he admires Zenos then it doesn't seem like he is genuine about his support of the faction seeking reform. We already know that Zenos didn't care much for anything related to Garlemald and tormented his own allies. Those he kept around and supported were manipulated purely to cause strife and division. Fordola and Yotsuyu were successful at that though Asahi seems to be the most devoted of all. Perhaps Varis is genuinely interested in reforming Garlemald? Garleans are described in the lore book as being efficiency driven, after all. Though we've yet to see much of that due to the 'crazies' being at the forefront for the most part.