Multiple out signals with single clock
Well, if your chip has an external memory interface that you aren't using then you might be able to do something a little bit naughty, presuming the external memory interface can be configured properly.  The idea is simple: connect all of the MOSI pins on the chips in parallel to the data bus pins with one MOSI pin per data pin, and conect all of the clock pins to the data bus clock, possibly with a buffer.  Then all you need to do is configure the external memory interface to run with the correct baud rate, and write the data to the memory mapped region with the DMA engine.  Naturally you will need to reformat the data so that bit 0 of each word corresponds to the first peripheral, bit 1 corresponds to the second one, and so on.