This.
Yes we all know the BBB is technically a powerless toothless organization. The thing is, it still matters to companies like Sony and MS. If you try calling again, threaten them about taking it to the BBB. If they don't help after that. *Actually* take it to the BBB. I had to do that after MS refused to refund me money after my account got hacked a few years back and what do you know, they fixed that real quickly.
Actually, it's a little bit more interesting than that, depending on the company.
With the BBB, there are some businesses that are "members" (technically called Accredited Businesses). Such businesses do have a legal contract with the BBB that they have to make a good faith effort to resolve any complaint that gets filed with a BBB office. If they do not, well... there are repercussions with that. Only the Sony Music branches are accredited, but there's a little bit of a rabbit hole problem if you have branches of a conglomerate that tries to resolve complaints and other branches that do not; they are going to want to know a little bit of info about that.
True, on a technical standpoint, since the BBB is non-legal and is a non-profit, Sony Computer Entertainment has no obligation to respond to a consumer complaint. But it still seems like they do respond to all of their complaints, usually by responding directly to the customer as soon as the BBB gets the complaint. So if this trend continues, if the OP files a complaint with that BBB office, that Sony branch should offer some kind of direct response to this issue.