Well, OK, then.
Went in to the bank with Phoenix when she opened her account to see if they could just attach me to it as well somehow. Sure enough, the woman opening her account said that as long as I had a BSN, there was no reason I couldn’t open my own account, despite what we’d been told earlier. So now we both have Dutch bank accounts and are just waiting to get our chip and pin cards in the mail (along with hardware two-factor authentication devices!).
She also handles insurance and we figured out that (not surprisingly) the insurance that we’d had to take out before we could rent our apartment (Dutch law) was overpriced. Not surprising since we had very few options to pick through that we could get from the US before we had our completed residence permits, BSNs or domestic bank accounts. We’re stuck for a year, but then we can switch to a plan that’s about a quarter the price.