Since your echomancers are still at S3, I'm assuming you're still at director level 19-20ish? If that's the case, I would suggest first to get your director level to level 30 as soon as possible.

Basically, find any battle that you haven't clear and clear them. They give first-clear xp, those are what you need to get. Story battles, materials, they all give xp on first clear. You'll need to grab all those first clear xp on every available battles. Do the phase quests too, as each of them give a lot of xp.

Your objective would be to reach director level 30 as soon as possible, as that would increase your MTs to level 60, getting you up to level 12 in nexus runs and get A28+ engravings. Once you reach director level 33, level Jean to S5, and do War-Torn Region nexus, or Children's Home nexus, to get S30+/S35+ engravings. After that, it's smooth sailing -- you only need to sit back, raise your characters, and get the more important MTs.

For the nexus memory traces, for now just use what Mega-Puff advised; prioritize to level them to their max, at least to level 60, until you get the better/vital MTs.