Update: @Doorknob made some important points and I agree with him. There need not be a limit on the number of users per box. Also, the criterion for helping new users doesn't necessarily have to be 4k rep. It could be a lower rep threshold or something like time spent on the site.
There have been discussions (1 2) on whether we should have a sandbox for Puzzling SE. Most people said no, because it would be difficult to correct a puzzle without knowing the answer. Moreover, people who help in correction will have an advantage over the other users.
Here is my suggestion.
Why don't we have a private sandbox? Each new user (with, say, below 400 rep) will be prompted (either optionally or by compulsion) to enter their puzzle (and even its answer, on request) into a new private box (or chat room, if we must exploit the existing site functionality only). Only trusted users (>4k rep) will be allowed to enter a box, and it will be declared that they entered a box when they do so. The trusted user(s) will discuss with the new user what the problems in the post is/are. If the new user is not being responsive or putting any efforts, a trusted user could state that and abandon the box temporarily. Otherwise, if the discussion is completed and the puzzle is posted on the site, the users who entered that particular box will not be allowed to reveal the answer or give hints to others. I would recommend that the number of users in a box should be either 1, 2 or 3, but you people could arrive at a conclusion on that.
I don't think we should recommend usage of this sandbox by experienced users, since we don't have that many trusted user(s) to handle the traffic. But I do feel it would be more helpful for new users to have someone they can actually chat and discuss their questions with, rather than just some curt comments and close votes on their posts.
Will it work? And please remember that if we go ahead with this idea, we need some users to actually volunteer for the work.