After 6mil vapor barrier in crawl space, moister gathering between insulation and flooring
It's best to not use faced insulation here for the reasons you've noted, But new insulation may not be necessary- you can carefully peel the face paper off and re-use what you have as long as it's not moisture-laden itself. Also, the ground sheet poly isn't exactly a waterproofing. It's purpose is to reduce, not eliminate, the moisture evaporating from the soil so normally having a foot of overlap between sheets is fine without taping. You should also have good crawlspace ventilation to go with this.

Phil