The reference to them living in 1645 on the rue du Pot d'Etain is almost certainly a veiled reference to the inventaire après décès for Adam, also filed with a notary in Montreuil-sur-Mer (and which I also requested from the archives):
https://en.geneanet.org/archival-registers/view/218839/37
Adam's baptismal record, burial record, and the baptismal records of 5 of his children are all in Montreuil-sur-Mer, so I don't think there's really any question where he lived. Section C of Montreuil-sur-Mer's 1810 cadastre shows this rue in the same place as that portion of the modern-day Rue Pierre Ledent south of its intersection with Rue due Thorin:
https://archivesenligne.pasdecalais.fr/v2/ad62/visualiseur/cadastre.html?id=365212285
https://www.openstreetmap.org/#map=19/50.46346/1.75988
Fundamentally, coming back to the original question as to whether the places should all be changed to Montreuil, Picardie, France, it seems like we have at least some indirect evidence for Montreuil, as their descendants were living there by 1600, and, as far as I can see, nothing for Bazinghen beyond the name matching the place, so I guess I'm having trouble understanding why this proposed change seems to be controversial? I don't include -sur-Mer in my proposal, as the official name didn't change until 2023:
https://www.legifrance.gouv.fr/jorf/id/JORFTEXT000046285138
Also, to clarify my prior comments about the lieu-dit, if you search the modern-day cadastre for the "LES TROIS MAISONS" Lieu-dit in Bazinghen, it shows some parcels immediately west of the village of Noirbernes (which itself is in the neighboring commune of Audembert), so it does still appear on current maps:
https://www.cadastre.gouv.fr/scpc/accueil.do