Most open backs dont leak enough sound to be annoying 5m away, and I do think the zen has enough juice to drive basic planars off balanced.
Zen Dac + he400i/s/4xx with a balanced cable upgrade would be my starter for immersion, for my personal taste.
t50rp with a k5pro and zmf pads would also be a good combo, and you can use both the amp and the pads with the m40x too, it will make those more immersive as well for when you need not to leak sound. Check out the zmf store I think they had a deal.
Fidelio x2, harmonicdyne helios/zeus are very easy to drive and good for immersion, check those out too.