The Headliner cloth has become loose across the whole front edge of the windshield about 4 inches back.

Need some advice on how to fix without replacing.

Replace it. The foam padding is rotting. The whole headliner will slowly sag in the near future. Cost is approx. $100-$200. Been there - done that (twice).,...offgas

What kinda of shop would replace headliners?

Most upholstery shops should be able to do it. I use a guy in Orlando who does them out of a roving van at the place of your choosing. He does a great job. Claims to have done 30,000 headliners over 35 years. He just did another one for me - 2006 Caravan about 2 weeks ago - $165.