Trema can't be oversouled, so no it's not necessary.

I don't believe it is every too late to start oversouling fiends to get The End garment grid. And there is no fiend that you only have once chance to oversoul. Every fiend except two can be found in the Via Infinito. The two exceptions are the two fiends in the Bevelle Underground, and they can be fought in Ch 5 as many times as you want. There are a few fiends that you have to fight as a boss battle, and then they become fightable in the Via Infinito, but there are only a few, and if you do all the side quests then you likely won't even have this problem.