If your old van didn’t have a bulkhead the difference they make to the noise level while driving so I don’t imagine you’d need to do anything.
Your plan is what I’ve done to other vans without bulk heads before with good results so I’d just do that. if you do want to go further then cover the roof in the same way with insulation and ply (assuming you’re not already) and look at some soft covering for the floor.
Getting a never van soon, and with the old one have put 2 layers of foam padding as used under laminate flooring, also stuffed the inside between the plywwod sides and the steel outside with fibreglass insulation, theres a steel bulkhead, would it make any difference to pannel this with an old duvet.
Any other ideas.