You do realize that the new series would "perpetually be in the old series' shadow" precisely IF they don't choose to completely and totally ignore all characters and move on....right?
They can't ignore the old characters. That's the problem. There's too much money, too much fandom, too much lore, too much everything. It's not like Dragon Age where you can just pick a different corner of Thedas and try something new, and even then, they bring people back in that series and have events follow a path based upon what a player says happened earlier on. Why should I believe that Mass Effect will be treated differently, especially with all of the investment that people have in it?
It's very easy to not have things be stuck in shadows. The best way is to acknowledge what happened, let ongoing things continue to happen, and move on. The Elder Scrolls offers a good example. Each game is very distinctly connected to the last, with a tapestry of narrative threads, but has all sorts of new things going on, too. Some things and people show up more than once, and it's acknowledged when it happens. Oblivion wasn't in Morrowind's shadow, and Skyrim wasn't in Oblivion's shadow. Granted, those are three separate games and not a trilogy, but it's easy to get invested into each one. What each provides is closure for the previous game. We know what happens after TESIII and what happens after TESIV. We don't have to know everything, but there are big questions and names that people want to know about, and we get answers, and it satisfies most people. They can do the same with Mass Effect. No, Shepard doesn't need to travel to nowhere in particular to be written off, but some kind of acknowledgement must be given, otherwise it'll be a rain cloud which hangs over the series until it gets answered.
And I think that answer will be a DLC or a new game.