And even then, given his rather memorable comment during afterlife, it would be as a boss, mentor or even just dispatcher, to the new crew. By all means, include the others. Ray would probably be spot on for researcher and active support, put a book that peter wrote on the coffee table in the break room, put a nice memorial to egon on the wall. There's no reason tully couldn't be the financial oversight, and hell; why not! Give Janine a nice promotion and make her the teams lawyer.
There's ways to include the old cast without requiring them suit up and start bustin'. They can have cameos and one liners and walk ons without being the central focus. We've already seen that they can do it and still make a good movie.