Matthew 6:6 and Private Prayers

My pastor has started a series through the Lord’s Prayer. In his introductory sermon he stressed two aspects of the text:
a) Prayer is expected, not optional.
b) Prayer should be genuine.
These are clear implications in the text. Prayer becomes a necessary dimension of spiritual growth. In the words of Dean Richard Lobs, “it is the most unnatural thing we will ever do in this world.” In Psalm 50:21 we find that God lacks nothing. This entails that we depend on every element of life to come from His sovereign providence.
In verse 6 we read:

But when you pray, go into your room and shut the door and pray to your Father who is in secret. And your Father who sees in secret will reward you.

This is a strange element indeed. Here in this text God makes a direct contrast with the hypocrites. This should not be seen as a proof-text for individualism. Rather, the contrast here is with the self-exalting prayer of the hypocrites. If one were to imitate the Pharisees, he would fall into the same sin, even he did not intend to do so. The Puritan Matthew Henry expounds:

Instead of praying in the synagogues and in the corners of the streets, enter into thy closet, into some place of privacy and retirement. Isaac went into the field (Gen. 24:63), Christ to a mountain, Peter to a housetop. No place amiss in point of ceremony, if it do but answer the end. Note, Secret prayer is to be performed in retirement, that we may be unobserved, and so may avoid ostentation; undisturbed, and so may avoid distraction; unheard, and so may use greater freedom.

My particular practice has been to find a Catholic or Anglican church in the area. There is always an open chapel. That may be a perfect place to pray in secret, furthermore, far away from the paragons of self-exaltation. For this one thing I know, no hypocrite or Pharisee will look for a generally empty chapel to pray.