We agree that a major part of praying without ceasing is directly connected to our attitude toward and with God, which is really in the context of what Paul was writing about.
We are to be thankful for everything, whether it's a sunset or the water coming out of the tap. We are to be joyful for all that God as done for us, and the insights He has given us, even in the face of all kinds of evil, and in that knowledge we can truly become a loving, compassionate, and joyful peacemaking child of God. When we enter this stage in our spiritual development, our whole being becomes a continual prayer.
This is also what John Wesley wrote about in his book, Christian Perfection:
"For, indeed, he 'prays without ceasing [1 Thessalonians 5:17]'; at all times the language of his heart is this: 'Unto thee is my mouth, though without a voice; and my silence speaketh unto thee.' His heart is lifted up to God at all times and in all places. In this he is never hindered, much less interrupted, by any person or thing. In retirement or company, in leisure, business, or conversation, his heart is ever with the Lord. Whether he lie down, or rise up, 'God is in all his thoughts'; he walks with God continually, having the loving eye of his soul fixed on Him, and everywhere 'seeing Him that is invisible [Hebrews 11:27].' "
In the Love of the Lord,
Frank and Mary