I would suspect you want what you want because the Foose folks have elevated it to the top.
PPG has been the standard in almost every genre' of vehicles for decades. I just had a 94 Camaro painted with the new water based PPG stuff and we are 10
months into it and it still looks assembly-line perfect.
Stripping the PPG primer off will be costly. It sounds like the paint shop you have chosen has already dropped-the-ball because the topcoat must be applied within a certain
time-window (something like 6 to 12 hours) for chemical crosslinking to take place. Otherwise every surface must be sanded or it won't stick. A mechanical bond is not near as good as chemical covalent bonds.
If I was getting a high end car painted, I'd let the paint shop use the brand they are used to. I'd personally download the Product Data Sheets for each product used from metal repair to metal prep, to primer to topcoat. I'd study them. Then I would require all the products to be from the same manufacturer and in their same Paint System. I would cover every tiny detail on the Product Data Sheets with my painter, especially adhering to application wait-times between coats and products. Pay attention to temperature and humidity specifications and have them provide proof that their booth fell within those specs.
I am prepping my body right now for paint. I am spending about 2 hours per square foot cleaning to bare metal with stainless wire brush on a grinder. Then I am lightly priming with PPG epoxy primer as I finish, in about 9 sq ft blocks. This will keep rust "bloom" from occurring until the whole car is finished. Then when my chosen paint shop starts work, they will remove my primer (probably by low pressure abrasive blasting with fine medium) immediately before applying their first primer coat.