Brother you kind of lost me...  What do you mean by replacement for the New Covenant?
The first covenant still stands, which is God's covenant with Abraham.  Right?  
The covenant with Moses which was the law and commandments, were done away with in Christ.  He fulfilled it.
So we are children of faithful Abraham.

When Abraham paid tithes to Melchisedec, there is no mention of a temple.

So today, even though we as God's people are a collective church, does not mean that a brick and mortar building led by a God fearing pastor, is of no relevance.  

Collectively meeting in a church building is important, if a good one can be found.  That way God's people can use their gifts to bless others as taught by Paul.

Think about this too brother, paying tithes can be to other Christian organizations that are doing good works for the Lord.

Blessings and peace.