Glenn is right on. The other issue is that the laminate will continue to peel and crack underneath...kind of like having a bad foundation. If you have a heat gun it will loosen the existing stuff.This will also be sharp as it comes apart..where your welding gloves...or kevlar fishing mitts.
Have plenty of ventilation...open windows in minus 20 degrees.
Or purchase new plywood and use the existing top as your template.
The wood front edges add a nice touch.
Try a kitchen showroom for some ideas.