I was looking up parts for an unrelated project and cam across
MAX3421. It's a USB controller that can act as a host. I didn't really read it in detail, but the datasheet specifically mentions using bit banging methods for its SPI interface. It's effectively a USB to SPI adapter. I have a feeling that the software will still be a challenge though.
I think it said that it only comes in QFN though (surface mount with pads on the bottom rather than leads). It might be hard to work with.