I think making the private instance from hard achievements accessible to friends is a great idea, and not just limited to Nex. I understand the concern of private instances bringing in too many items but locking it behind hard diary (which also entices more people to complete them) on top of the GE tax + deleting items, should alleviate most concerns.
You can also make it so completing higher tiers allows more people to join, to help further reduce any mass farming that you think may happen. For example, hard = 3-4 players max, elite = 5-6, master = 10, grandmaster = 20 (or unlimited due to the difficulty of this achievement, and would be great for clan events).
Also if this question could be discussed on the stream today that'd be amazing. Can we extend private instances to other gwd bosses/other bosses in general, locking it behind combat diary with higher tiers = more players can join? u/JagexLight