My position (which is also that of the PCA and OPC) is "close" communion. The table is fenced, and requirements are laid down, but the Session does not have to examine each person communing.
I have seen John Murray's arguments before, and they did not impress me then. His position boils down to "we might possibly make a mistake, so we should be as conservative and restrictive as possible; and if someone worthy is barred, he should appreciate our being diligent and get over it."
If a person is a member in good standing of a true church - and it is recognized as such by the church communing - the Session of the communing church has no business second guessing the proper judiciary. It is a withholding of the means of grace and a denial of connectionalism.
Question that I have regarding "long term visitors" is what should a session do if a church has people who not members of any church but are visiting your church for months if not years without making a formal profession of faith before the session. For instance the Smiths are not members of any church but are consistent visitors each week for the last 2-3 years. They've been approached about membership, have denied it, but partake of the Lord's Supper monthly.
Thoughts....