Hi Gale

I wish that there was a non chemical formula that destroyed the weeds and the roots but I know of none at this time.  The vinegar formula does not eradicate the roots and seeds which will continue sprouting new chickweed. 

To remove the plant begin by pulling as much of the plant as you can. Then use a spot treatment that contains Glyphosate over a couple of weeks to get rid of the remaining chickweed plants.

Spread a pre-emergent heavily in the area this fall  and again in the early spring. That should prevent the growth of new plants from seed that the chickweed had dropped.

Let me give you some excellent references on landscape, yard and garden information. The Wood County OSU Extension Office located at 639 S Dunbridge Rd#1, Bowling Green Ohio 432402.  Telephone number is<personal data hidden>. They have knowledgeable staff available to answer questions and assist you. https://ohioline.osu.edu is an internet site filled with informative fact sheets. https://bygl.osu.edu is a weekly newsletter that sends our information regarding lawns and landscape throughout the growing season. It is a subscription service (free) and very informative.

I wish you the best in cleaning up the church labyrinth. I hope I have been helpful.

Sincerely,

Mike Heys, Franklin County Master Gardener