My network also includes private and specialized lenders. Before pointing you toward private financing, I check whether a traditional or specialized lender can do the job, because it costs considerably less.
Your bank said no and offered no alternative. Finding a private lender on your own means signing a short, expensive, technical agreement with nothing to compare it against. If private is still the right option, I compare lenders on what you receive, not just the rate: fees, brokerage, prepaid interest, mortgage rank, and renewal conditions. And if the structure doesn’t hold up, I say so.