Thank you Bradley for your very insightful suggestions. It had never occurred to me to take a series of measurements and then post-process to look for a trigger condition. Working with the DAQ6510, with its powerful on-instrument processing, takes some getting used to and causes us to rethink our old ways of doing things.
I tried a solution similar to what you suggested, basically a digitized acquisition of X measurements and then analyzed them looking for positive pulses which then gave me the pulse widths I needed. I didn't use the limits/statuses as you suggested, mostly because I was not familiar with those at all, instead I just examined the reading values directly. I found the post-processing of 1M points did take some time (~7 seconds) which was longer than I'd expected but not a problem in this application because I'm just scanning temperatures.
As a exercise I went a bit further and experimented with using the trigger model as you hinted at, but this didn't really help with the processing time as I still needed to iterate through the readings array to find the edges. (I used "LoopUntilEvent" with a rising edge condition.) Since I knew beforehand the width of the pulse(s) I could reduce the sample count to much less than 1M and this sped things up considerably, to around 25ms which makes this solution feasible for future use on scanning other signal types beyond slowly changing temperatures.
Thank you very much for your suggestions, and if you do think of any ways to employ the trigger model I'd love to hear about them!