Right- the event triggering the DAC change is the SPI SYNC pin, but this is simultaneous with SPI clock and MOSI. So the problem is the same- I can't get that sync pin (or the other SPI controls) to synchronize with the fast square wave.
Ok. So, your "SPI SYNC" signal goes down, then you transfer data through SPI, then "SPI SYNC" goes up which triggers DAC reload. Is that correct?
Then, instead of "SPI SYNC" from the MCU, connect your 100 kHz input signal (assuming it's 50% duty). Also wire the same signal to MCU. Create an interrupt on the falling edge of the 100 kHz signal. When processing this interrupt, transmit SPI. You have 5 us for this, which is still plenty. And the SPI timing doesn't matter.
The whole thing will work as follows:
On the falling edge of 100 kHz signal the DAC sees the SYNC going down. At the same time, the interrupt happens in your MCU, you start transmitting SPI and quit the interrupt. Some time later, the SPI transmission completes, the DAC receives the data, but the DAC does not update the output and waits until it gets a rising edge of SYNC.
On the rising edge of 100 kHz signal, DAC sees is as SYNC going up and updates the output. The change of the DAC output is thereby synchronized to your 100 kHz signal directly. Hence you don't need to create a copy of it.