Transfer 24 bit data over SSI

I need to get a 24 bit ADC result from an AD7766 into a TM4C1294 over the QSSI I/F.
I can't bit-bang the results out as I'm sampling @ 51 kHz and that would take up too much processor time.

Is there a way I could get the processor, acting as a master perhaps, to clock the 24 bits in as 3 groups of eight? The ADC is happy so long as I keep CS# low it will clock out from MSB->LSB. I think my problem will be framing the 8 bit chunks at the processor.

I've actually got an eval board for the AD7766 on order, so in a week or so I'll be able to 'suck it and see'. But for now, has anyone ever tried anything like this?

Or have I wandered wayyyy off the reservation on this one?