set up saved viewpoints that you will use to specifically push to Procore for models.
These need to have section boxes set up as it helps in the publishing process - especially if you are slicing out floors.
Best practice is to save sectioned views, by floor, from 0.1" below bottom of slab below to 0.1" to bottom of slab above, for each floor for coordination
The views need to have the OVERRIDE APPEARANCE option NOT checked.
uncheck the global override appearance box in the viewpoint defaults in the settings of Navisworks.
This does not mean that other views in your model can't have the override appearance set - it's just the global one and the views that you are going to publish.
Publishing to Procore
Select the view
Reset all appearances
Run appearance profile
Right click on the view and choose update
Publish to Procore
What happens is that when you update that view you want to publish - that locks the colors into that view (even if override appearances aren't checked) and pushes that to Procore.
Currently, as part of the publish process - Procore reads the permanent color which is the saved color overrides and transparencies when publishing.