High Step-up Ratio DC-DC Convert (12V-to-150V) - Boost, Flyback, Coupled-inductor Boost?
As you've already stated yourself, you'll have a hard time finding an OTS flyback transformer. Custom made and I'd prefer this solution too.

Another approach that I would personally pursue, is a 2-stage boost converter. Duty factors are within reason and first step will be easy. Second step in principle is just as easy, but the trouble will be to find a controller that can handle the high output voltages. Little chance of finding one with integrated FET. This approach can use shielded inductors. Small if high switching frequency is used.