I don't know if you'll be able to use your own multiplexing. SCXI can certainly handle this, and if you want to use your own signal conditioning, you can just get a voltage input card (SCXI) and use your signal conditioning into it.
While you can probably use your multiplexing board by writing code to make it switch inputs, the SCXI makes all that seamless, and has a faster response time, so it may be more advantageous from a time and cost standpoint just to start with SCXI. It automatically routes the signals to one channel for you.
Since you state that your acquisition rates would be somewhere in the 1000 Hz range (around a millisecond per point), you can stream the data to disk in engineering units, although you most certainly can store it in binary
format if you wish.
As far as speed, SCXI lets you scan (acquire) at 333 Ksamples/sec divided by the number of channels. So, at 64 channels, your maximum scan rate would be 333000/64 = 5203 samples per second. Make sure that this would be fast enough for you, especially if you plan on having more than 64 channels, as you have stated.
Mark