I don't know if that would be possible with the SR400. First, the mimimum dwell time is 2 ms (time for the counts to be stored, reset the circuitry, etc). Also, the max storage size for each channel is 2000 points/measurements, so you would only be able to record for ~30 minutes with your specs.
However, I have a VI that circumvented the 2000 point limit. It was for a photobleaching experiment that ran over a couple days, but it was not included above. Basically, it would integrate for some period (1 sec in my case), download that single point, delay for another time period, and then repeat for a large number of iterations. But, I still think it can the min delay between measurements was limited to 500 ms or so. It's at work, but I can look tomorrow.
If you can tolerate the 2 ms dwell time, the SR400 can be programmed easily with the SubVIs above. I think you would need to use Gate.VI to set the gates for each channel. I always intergrated over 1 second, so I just used the internal trigger.